the large hadron collider ( lhc ) at cern , geneva , switzerland , will be upgraded in two phases , resulting in ten times higher luminosity .the atlas detector is one of the two major experiments at the lhc .for the first phase of the luminosity upgrade , the plan is to install a new layer of pixel detector inside the present pixel detector to compensate for the expected degradation due to the intense radiation . we have designed three asics for possible applications in the optical links for the new pixel layer .the prototype asics were fabricated using a 130 nm cmos 8rf process .the asics contain three circuit blocks  ; a vcsel driver ( optimized for operation at 640 mb / s and 3.2 gb / s ) , a pin receiver with a clock and data recovery circuit capable of operation at 40 , 160 , or 320 mb / s , and a clock multiplier ( two versions ) designed to operate at 640 mb / s .the clock multiplier is needed to produce a higher frequency clock to serialize the data for transmission .all circuitries were designed following test results and guidelines from cern on radiation tolerant design in the 130 nm process used  .we have characterized the asics in the lab followed by an irradiation with 24 gev protons at cern .the results are summarized below .all asics tested were packaged for the irradiation and therefore we experienced some speed degradation due to the added stray capacitance of the packaging .the two vcsel driver circuits in the test chip have similar architecture ; one optimized for 640 mb / s with higher drive current and the other for 3.2 gb / s with lower current .each consists of a 1.5 v lvds receiver circuit , a 1.5 to 2.5 v logic converter circuit , and a 2.5 v vcsel driver circuit .both vcsel drivers allow for adjustable bias and modulation currents and contain circuitry to reduce switching noise on the power supply lines .the lvds receiver was designed using the standard thin oxide transistors that operate with a 1.5 v supply .the use of the of the thin oxide transistors allowed us to not only achieve higher bandwidth over the thick oxide transistors but also produce a circuit that could be used by other members of our community developing chips which operate with a single 1.5 v supply .we used a 2.5 v supply for the driver circuitry because most commercially available vcsels require bias voltages greater than 2 v to produce suitable output optical power .the driver portion of the chips were therefore designed using the thick oxide transistors available in the 130 nm process .previous results from cern have shown that thin oxide transistors designed using conventional layout techniques exhibit radiation tolerance suitable for slhc applications . however , conventionally designed thick oxide transistors are not suitably radiation tolerant .all of the thick oxide transistors were therefore designed using an enclosed structure .four prototype asics were packaged and the performance was satisfactory up to 1 gb / s .the performance at higher speeds could not be sufficiently evaluated due to the packaging parasitics .these tests also verified the operation of the lvds receiver up to 1 gb / s . during the irradiation ,each driver asic was connected to a 25  resistor instead of a vcsel to allow testing of the degradation of the chip alone .the duty cycle of the output signal and the current consumption of the lvds receiver remained constant during the irradiation .however , we observed significant decrease in the vcsel driver circuit current consumption and the output drive current .it should be noted that the decrease in the drive current could be compensated by adjusting the control current but this option was not used during the irradiation in order to study the degradation under the same condition .post - irradiation analysis indicates that there is no other significant degradation and the decreases in the vcsel driver current is now understood. figure [ iv ] shows the iv curves of a pmos transistor fabricated in the thick oxide technology before and after irradiation .the iv characteristic before the irradiation is well reproduced by the simulation .a shift is observed after the irradiation and is well reproduced by the simulation after including a 175 mv threshold shift .the threshold shift is significantly smaller in the nmos transistors .the present current mirror in the driver circuit uses both type of transistors and thus is sensitive to the different threshold shifts .the plan is to use pmos transistors only in the future design .the pin receiver / decoder contains a trans - impedance amplifier , limiting amplifier , bi - phase mark ( bpm ) decoder with clock recovery , and lvds drivers to send the decoded data and recovered clock off the asic .all transistors are fabricated with thin oxide , allowing the asic to run with a 1.5 v power supply .the clock and data recovery is accomplished using a delay locked loop that contains networks of switchable capacitors in the delay stages allow for the three operating frequencies , 40 , 160 , and 320 mb / s . however , due to insufficient time to optimize the design , the asics operate at somewhat lower speed and require higher threshold currents to achieve a low bit error rate ( ber ) .other than these two limitations , the performance of the asics is satisfactory , including clock jitter , duty cycle , rise / fall time , and high / low levels of the lvds drivers .  for the irradiation ,the asics were tested in two different setups of four asics each .the first setup was purely electrical while the second setup involved a pin diode so that we could decouple the electrical and optical degradations . in both setups ,the decoded data were transmitted to the control room using 20 m of coax . in the first setup ,40 mb / s bpm signals were transmitted over 20 m of coax to the asics .the long cable precluded testing at higher speed . in the second setup , we sent 40 mb / s bpm signal via a fiber to a pin diode coupled to an asic .for both setups , we observed single event upset during the spill but observed no degradation in the threshold for error / s as a function of dosage .we also monitored the ber vs. pin current during the irradiation .the ber decreased with larger pin current and was higher for an asic coupled to a pin diode as expected ( fig .[ ber ] ) .the current consumption was constant during the irradiation .detailed post - irradiation analysis reveals no significant degradation in the overall performance .the clock multiplier circuits consist of charge pump / ring oscillator phase locked loops ( pll ) with dividers in the feedback loop .one circuit performs a frequency multiplication of 16 and the other a multiplication by 4 , both yielding a 640 mhz clock .the multipliers are designed using thin oxide transistors and are powered by a single 1.5 v supply .the multiplier circuits share a common 50  driver and lvds receiver enabling testing of only one multiplier at a time .an additional switching network allows the recovered clock from the pin receiver prototype to be routed to either multiplier to allow for testing of how the received signal jitter is coupled to the multiplied clock .four multipliers were packaged for the irradiation .all asics functioned well with clock jitter of 8 ps ( 0.5% ) . during the irradiation, we observed that the clocks of two asics lost lock and power cycling was needed to resume operation at 640 mhz .this problem is not yet understood .detailed post - irradiation analysis also reveals no significant degradation in the overall performance .we have designed prototype asics using the 130 nm process to enhance the radiation - hardness .the submission has been mostly successful .we irradiated the asics to a dose of 70 mrad and observed no significant degradation except in the vcsel driver .post - irradiation analysis indicates that there is a significant threshold shift in the pmos transistors fabricated in the thick oxide technology for the operation at 2.5 v to drive the vcsel .an improved version of the asic will be submitted implementing what we learned from the study .this work was supported in part by the u.s .department of energy under contract no .de - fg-02 - 91er-40690 .the authors are indebted to m. glaser for his tireless assistance in the use of the t7 irradiation facility at cern .

Abstract: we have designed three asics for possible applications in the optical links of a new layer of pixel detector in the atlas experiment for the first phase of the lhc luminosity upgrade . the asics include a high - speed driver for the vcsel , a receiver / decoder to decode the signal received at the pin diode to extract the data and clock , and a clock multiplier to produce a higher frequency clock to serialize the data for transmission . these asics were designed using a 130 nm cmos process to enhance the radiation - hardness . we have characterized the fabricated asics and the submission has been mostly successful . we irradiated the asics with 24 gev / c protons at cern to a dosage of 70 mrad . we observed no significant degradation except the driver circuit in the vcsel driver fabricated using the thick oxide process in order to provide sufficient voltage to drive a vcsel . the degradation is due to a large threshold shifts in the pmos transistors used .


the relay channel was introduced by van der meulen in 1971 . in this setup ,a single transmitter with channel input communicates with a single receiver with channel output , where the superscript denotes the length of a vector .in addition , an external transceiver , called a relay , listens to the channel and is able to output signals to the channel .we denote the relay output with and its input with .this setup is depicted in figure [ fig : relay_setup ] .   in cover & el - gamalintroduced two relaying strategies commonly referred to as decode - and - forward ( daf ) and estimate - and - forward ( eaf ) . in dafthe relay decodes the message sent from the transmitter and then , at the next time interval , transmits a codeword based on the decoded message .the rate achievable with daf is given in ( * ? ? ? * theorem 1 ) :  [ thm : ceg_daf ] _ ( achievability of ( * ? ? ? * theorem 1 ) ) for the general relay channel any rate satisfying for some joint distribution , is achievable ._  we note that for daf to be effective , the rate to the relay has to be greater than the point - to - point rate i.e. otherwise higher rates could be obtained without using the relay at all . for relay channels where daf is not useful or not optimal , proposed the eaf strategy . in this strategy , the relay sends an estimate of its channel input to the destination , without decoding the source message at all. the achievable rate with eaf is given in ( * ? ? ?* theorem 6 ) :  [ thm : ceg_eaf ] _ ( ( * ? ? ? * theorem 6 ) ) for the general relay channel any rate satisfying for some joint distribution , where , is achievable . _  of course , one can combine the daf and eaf schemes by performing partial decoding at the relay , thus obtaining higher rates as in ( * ? ? ?* theorem 7 ) .   in recent years, the research in relaying has mainly focused on multiple - level relaying and the mimo relay channel . in the context of multiple - level relaying based on daf ,several daf variations were considered . in cover & el - gamal s block markov encoding / succesive decoding daf method was applied to the multiple - relay case .later work , and applied the so - called regular encoding / sliding - window decoding and the regular encoding / backward decoding techniques to the multiple - relay scenario . in daf strategy was applied to the mimo relay channel .the eaf strategy was also applied to the multiple - relay scenario .the work in , for example , considered the eaf strategy for multiple relay scenarios and the gaussian relay channel , in addition to considering the daf strategy . also considered the eaf strategy in the multiple - relay setup .another approach applied recently to the relay channel is that of iterative decoding . in three - node network in the half - duplex regime was considered . in the relay case , uses a feedback scheme where the receiver first uses eaf to send information to the relay and then the relay decodes and uses daf at the next time interval to help the receiver decode its message .combinations of eaf and daf were also considered in , where conferencing schemes over orthogonal relay - receiver channels were analyzed and compared . both and focus on the gaussian case .an extension of the relay scenario to a hybrid broadcast / relay system was introduced in in which the authors applied a combination of eaf and daf strategies to the independent broadcast channel with a single common message , and then extended this strategy to the multi - step conference . in used both a single - step and a two - step conference with orthogonal conferencing channels in the discrete memoryless framework .a thorough investigation of the broadcast - relay channel was done in , where the authors applied the daf strategy to the case where only one user is helping the other user , and also presented an upper bound for this case .then , the fully cooperative scenario was analyzed .the authors applied both the daf and the eaf methods to that case .one important instance of the relay channel we consider in this work is the gaussian relay channel with coded modulation .this scenario is important in evaluating the rates achievable with practical communication systems , where components in the receive chain , such as equalization for example , require a uniformly distributed finite constellation for optimal operation . in gaussian relay channel scenarios ,most often three types for relaying techniques are encountered :  * the first technique is decode - and - forward .this technique achieves capacity for the physically degraded gaussian relay channel ( see ) , and also for more general relay channels under certain conditions ( see ) . * the second technique is estimate - and - forward , where the auxiliary variable is assigned a gaussian distribution .for example , in a gaussian auxiliary random variable ( rv ) is used in conjunction with time - sharing at the transmitter , and in the ergodic capacity for full duplex transmission with gaussian eaf is obtained . *the third technique is linear relaying , where the relay transmits a weighted sum of all its previously received inputs .an important subclass of this family of relaying functions is when the relay transmits a scaled version of its input .this method is called amplify - and - forward , and was later combined with daf to produce the decode - amplify - and - forward method of .several recent papers consider the gaussian relay channel with coded modulation . in author considered variations of daf for different practical systems . in daf andamplify - and - forward were considered for coherent orthogonal bpsk signalling , and in a practical construction that implements a half - duplex eaf coding scheme was proposed .  as indicated by several authors ( see ) it is not obvious if a gaussian relay function is indeed optimal . in this paperwe show that for the case of coded modulation , there are scenarios where non - gaussian assignments of the auxiliary rv result in a higher rate than the commonly applied gaussian assignment .in the following we summarize the main contributions of this work :  * we give an intuitive insight into the relay channel in terms of information flow on a graph , and show how to obtain ( * ? ? ? * theorem 6 ) from flow considerations . using flow considerationswe also obtain the rate of the eaf strategy when the receiver uses joint - decoding .a similar expression can be obtained by specializing the result of to the case where the relay does not perform partial decoding .we then show that joint - decoding does not increase the maximum rate of the eaf strategy , and find the time - sharing assignment that obtains the joint - decoding rate from the general eaf expression .we also present another time - sharing assignment that always exceeds the joint - decoding rate . *we introduce an achievable rate expression for the multiple relay scenario based on eaf , that is also practically computabe . as discussed in section [ sec : relay_strategies ] , in the noisy relay " case eaf outperforms daf .however , for the multiple relay scenario there is no explicit , computationally practical expression based on eaf that can be compared with the daf - based result presented in , so that the best strategy can be selected . as indicated in (* remark 22 , remark 23 ) , applying general eaf to a network with an arbitrary number of relays is computationally impractical due to the large number of constraints that characterize the feasible region .therefore , it is interesting to explore a computationally simple assignment that allows to derive a result that extends to an arbitrary number of relays .we also provide an explicit numerical example to demonstrate that indeed there are cases where multi - relay eaf outperforms the multi - relay daf .* we consider the optimization of the eaf auxiliary random variable for the gaussian relay channel with an orthogonal relay .we consider the coded modulation scenario , and show that there are three regions : high snr on the source - relay link , where daf is the best strategy , low snr on the source - relay link in which the common eaf with gaussian assignment is best , and an intermediate region where eaf with hard - decision per symbol is optimal .for this intermediate snr region we consider two kinds of hard - decisions : deterministic and probabilistic , and show that each one of them can be superior , depending on the channel conditions . *lastly , we consider the cooperative broadcast scenario with a multi - step conference .we present a general rate region , extending the marton rate region of to the case where the receivers hold a -cycle conference prior to decoding the messages .we then specialize this result to the single common message case and obtain explicit expressions ( without auxiliary rvs ) for the two - step conference .the rest of this paper is organized as follows : in section [ sec : timeshare_single ] we discuss the single relay case .we consider the eaf strategy with time - sharing ( ts ) and relate it to the eaf rate expression for joint - decoding at the destination receiver . in section [ sec : multiplerelays ] we present an achievable region for the multiple - relay channel , and in section [ sec : gauss_relay ] we examine the gaussian relay channel with coded modulation . in section [ sec : application_multi_step ] we investigate the general cooperative broadcast scenario , and obtain an explicit rate expression by applying ts - eaf to the general multi - step conference .finally , section [ sec : conclu ] presents concluding remarks .first , a word about notation : we denote discrete random variables with capital letters e.g. , , and their realizations with lower case letters , .a random variable takes values in a set .we use to denote the cardinality of a finite discrete set , and denotes the probability distribution function ( p.d.f . ) of on . for brevity we may omit the subscript when it is obvious from the context .we denote vectors with boldface letters , e.g. , ; the element of a vector is denoted by and we use where to denote .we use to denote the set of -strongly typical sequences w.r.t .distribution on , as defined in ( * ? ? ?5.1 ) and to denote the -weakly typical set as defined in ( * ? ? ?we also have the following definitions :  [ def : relay_channel ] the _ discrete relay channel _ is defined by two discrete input alphabets and , two discrete output alphabets and and a probability density function giving the probability distribution on for each .the relay channel is called _ memoryless _ if the probability of a block of transmissions is given by .  in this paperwe consider only the memoryless relay channel .[ def : code ] a _ code _ for the relay channel consists of a source message set , a mapping function at the encoder , a set of relay functions where the relay function maps the first channel outputs at the relay into a transmitted relay symbol at time .lastly we have a decoder   [ def : perr ] the _ average probability of error _ for a code of length for the relay channel is defined as where is selected uniformly over .a rate is called _ achievable _ if there exists a sequence of codes with as .consider the following assignment of the auxiliary random variable of theorem [ thm : ceg_eaf ] : under this assignment , the feasibility condition of becomes and the rate expression becomes clearly , maximizing the rate implies maximizing subject to the constraint  ] , is achievable ._  now , consider the following distribution chain : we note that this extended chain can be put into the standard form by letting .after compression of into , there is a second compression operation , compressing into .the output of the second compression is used to facilitate cooperation between the relay and the destination .therefore , the receiver decodes the message based on and , repeating exactly the same step as in the standard relay decoding , with replacing .then , the expressions of theorem [ thm : ceg_eaf ] become now , applying ts to with the expressions in and become combining this with the constraint  ] is selected such that . the approximation in ( a )is because for small , and , and for large , both and . hence dy\\         & = & \frac{1}{2\pr(y_1>0 ) } \left[h(n ) + \log_2 \left(2\pr(y_1>0)\right)\right],\end{aligned}\ ] ] and using and , we obtain therefore , at low snr , and become independent .then , and the information rate becomes ( see appendix [ appndx : appndxhd - eaf - highsnr ] ) where is the discrete entropy for the specified discrete distribution and .now , consider the feasibility condition : where ( a ) follows from the independence of and at low snr , see appendix [ appndx : appndxhd - eaf - highsnr ] . therefore , for low snr , we set and the rate becomes   for the gq - eaf we first approximate at low snr starting with : as in the region when is significant , for both or .we conclude that as the direct snr approaches 0 , and become independent .now , the rate is given by : the feasibility condition becomes : with .\ ] ]  for dhd , as we have where ( a ) follows from the independence of and as and the fact that is a deterministic function of , combined with the fact that given , and are independent .the feasibility condition becomes because is not a monotone function of we have to optimize over to find the actual rate .  as can be seen from the expression for hd - eaf , when the snr on the direct link decreases , the capacity of the conference link acts as a scaling factor on the rate of the binary channel from the source to the relay .  in figure[ fig : low - direct - snr ] we plotted the information rate for dhd , hd - eaf , gq - eaf and daf ( which coincides with the upper bound ) . comparing the three eaf strategies we note that dhd , which at intermediate snr on the source - relay channel performs well for , has the worst performance at low snr up to . at , dhd becomes the best technique out of the three . for and highsnr on the source - relay channel , hd - eaf outperforms both dhd and gq - eaf . for low snr on the source - relay channel, gq - eaf is again superior .we make the following observations :  * as noted at the beginning of this section , for low snr on the source - relay link , gq - eaf outperforms ts - dhd . to see why , consider the distribution of : where the approximation is obtained using the first order taylor expansion , and the fact that for large values of , dominates the expression .therefore , as , approaches a zero - mean gaussian rv : . as discussed in (13.1 ) , the closer the reconstruction variable is to the original variable , the better the quantization performance are expected to be .therefore it should be natural to guess that gq will perform better at low relay link snr .* at the other extreme , as , consider the daf strategy : as , have that \times\\       &  & \qquad \qquad \qquad       \log_2\left(\frac{1}{2}\left[g_{y_1}(g\sqrt{p},{\sigma_1 ^ 2 } ) + g_{y_1}(-g\sqrt{p},{\sigma_1 ^ 2})\right ]       \right)dy_1\\     & \stackrel{g \rightarrow \infty}{\approx } &  1 - \int_{y_1 = -\infty}^{\infty } \frac{1}{2}g_{y_1}(g\sqrt{p},{\sigma_1 ^ 2 } )       \log_2 g_{y_1}(g\sqrt{p},{\sigma_1 ^ 2 } ) dy_1 \\     &  & \qquad \qquad \qquad - \int_{y_1 = -\infty}^{\infty } \frac{1}{2}g_{y_1}(-g\sqrt{p},{\sigma_1 ^ 2 } )       \log_2 g_{y_1}(-g\sqrt{p},{\sigma_1 ^ 2 } ) dy_1\\     & = & 1 + h(n_1 ) ,   \end{aligned}\ ] ] and therefore , hence , which is the maximal rate .therefore , as daf provides the optimal rate .* we can expect that at intermediate snr , methods that balance between the soft - decision per symbol of gq - eaf and the hard - decision on the entire codeword of daf , will be superior to both .furthermore , we believe that as the snr decreases , increasing the cardinality of accordingly will improve the performance .in this section we consider the cooperative broadcast ( bc ) scenario . in this scenario ,one transmitter communicates with two receivers . in its most general form ,the transmitter sends three independent messages : a common message intended for both receivers and two private messages , one for each receiver , where all three messages are encoded into a single channel codeword .each receiver gets a noisy version of the codeword , at and at . after reception , the receivers exchange messages in a k - cycle conference over noiseless conference links of finite capacities and .each conference message is based on the channel output at each receiver and the conference messages previously received from the other receiver , in a similar manner to the conference defined by willems in  for the cooperative mac .after conferencing , each receiver decodes its message .this scenario is depicted in figure [ fig : three_msg_bc ] .this setup was studied in for the single common message case over the independent bc ( i.e. ) , and in for the general setup with a single cycle of conferencing .we use the standard definition for the discrete memoryless general broadcast channel given in .we define a cooperative coding scheme as follows :  _ a -admissible k - cycle conference _ consists of the following elements :  1 . message sets from to , denoted by , , ... , , and message sets from to , denoted by , , ... , .message set consists of messages and message set consists of messages . mapping functions , one for each conference step from to : and mapping functions , one for each conference step from to : where .the conference rates satisfy :   _ a code _ for the general broadcast channel with a common message and two independent private messages , consists of three sets of source messages , , and , a mapping function at the transmitter , a -admissible -cycle conference , and two decoders ,   the _ average probability of error _ is defined as the average probability that at least one of the receivers does not decode its message pair correctly : where we assume that each message is selected uniformly and independently over its respective message set .we first present the general result for the cooperative broadcast scenario with a -cycle conference .denote with and .let and be the private rates to and respectively , and let denote the rate of the common information .then , the following rate triplets are achievable :  [ thm : multi - step - general - bc ] _ consider the general broadcast channel with cooperating receivers , having noiseless conference links of finite capacities and between them .let the receivers hold a conference that consists of cycles .then , any rate triplet satisfying _  subject to ,    for some joint distribution is achievable .the cardinality of the auxiliary random variables are bounded by :    the coding strategy is based on combining the bc code construction of , after incorporating the common message into the construction , with the -cycle conference of .the transmitter constructs a broadcast code to split the rate between the three message sets .this is done independently of the relaying scheme .each receiver generates its conference messages according to the construction of .after cycles of conferencing each receiver decodes its information based on its channel output and the conference messages received from the other receiver .* fix all the distributions in . fix and let .let be a positive number whose value is determined in the following steps .let .let \delta}^{(n)} ] , where as and . *pick sequences from \delta}^{(n)} ] , and we have that and . * partition the set into subsets , , let +  ] . * for each triplet consider the set by ( * ? ? ?* lemma on pg .121 ) , we have that taking large enough we can make for any arbitrary , as long as + + note that the individual rate constraints are required to guarantee that the sets and are non - empty .* for each , we pick a unique pair of , .the transmitter generates the codeword according to + . when transmitting the triplet the transmitter outputs .* for the first conference step from to , generates a codebook with codewords indexed by according to the distribution : . uniformly and independently partitions the message set into subsets indexed by .denote these subsets with .* for the first conference step from to , generates a codebook with codewords indexed by for each codeword , , in an i.i.d .manner according to . uniformly and independently partitions the message set into subsets indexed by .denote these subsets with .* for the conference step from to , considers each combination of , . for each combination, generates a codebook with messages indexed by , according to the distribution . uniformly and independently partitions the message set into subsets indexed by .denote these subsets with . * the codebook for the conference step from to generated in a parallel manner for each combination of , . needs first to decode the message sent from at the cycle .to that end , uses , the index received from at the conference step . in decoding assume that all the previous were correctly decoded at .we denote the sequences corresponding to by + , and similarly define .* first generates the set defined by : * then looks for a unique such that .if there is none or there is more than one , an error is declared . * from an argument similar to , the probability of error can be made arbitrarily small by taking large enough as long as here , , since for the first conference message from to no decoding takes place .  in generating the conference message to , it is assumed that all the previous messages from were decoded correctly .* looks for a message such that from the argument in , the probability that such a sequence exists can be made arbitrarily close to by taking large enough as long as * looks for the partition of into which belongs .denote the index of this partition with .* transmits to through the conference link .   using similar arguments to section [ sec : decencmultisteprgood ] , we obtain the following rate constraints :* decoding at can be done with an arbitrarily small probability of error by taking large enough as long as * encoding can be done with an arbitrarily small probability of error by taking large enough as long as    first consider the bounds on , : this can be satisfied only if hence + 2k{\epsilon}\nonumber\\           & = &  \sum_{k = 1}^{k } i\left({\hat{y}}_1^{(k)},{\hat{y}}_2^{(k ) } ; y_1\big| y_2 , { \hat{y}}_1^{(1)},{\hat{y}}_1^{(2)}, ... ,{\hat{y}}_1^{(k-1 ) } ,             { \hat{y}}_2^{(1)},{\hat{y}}_2^{(2)}, ...,{\hat{y}}_2^{(k-1)}\right ) + 2k{\epsilon}\nonumber\\           \label{eqn : constr_c12_general_bc }           & = &  i\left ( { \hat{y}}_1^{(1)},{\hat{y}}_1^{(2)}, ...,{\hat{y}}_1^{(k ) } ,             { \hat{y}}_2^{(1)},{\hat{y}}_2^{(2)}, ... ,{\hat{y}}_2^{(k)};y_1\big| y_2\right ) + 2k{\epsilon } ,     \end{aligned}\ ] ] and similarly this provides the rate constraints on the conference auxiliary variables of and . uses and received from , to decode as follows :  * looks for a unique message such from the point - to - point channel capacity theorem ( see ) , this can be done with an arbitrarily small probability of error by taking large enough as long as denote the decoded message .now decodes by looking for a unique such that if a unique such exists , then denote the decoded index with .now looks for the partition of into which belongs and sets to be the index of that partition : .similarly to the proof in ( * ? ?* ch 14.6.2 ) , assuming successful decoding of , the probability of error can be made arbitrarily small by taking large enough as long as which is satisfied by construction .   repeating similar steps for decoding at we get that decoding can be done with an arbitrarily small probability of error by taking large enough as long as and assuming successful decoding of , decoding with an arbitrarily small probability of error requires that which again is satisfied by construction .finally , collecting , , , and give the achievable rate constraints of theorem [ thm : multi - step - general - bc ] , and and give the conference rate constraints of the theorem .   in the single common message cooperative broadcast scenario , a single transmitter sends a message to two receivers encoded in a single channel codeword .= 0.6  this scenario is depicted in figure [ fig : broadcast - cooperation - common ] .after conferencing , each receiver decodes the message . for this setupwe have the following upper bound :  [ prop : common_upper ] _ ( ( * ? ? ?* theorem 6 ) ) _ _ consider the general broadcast channel with cooperating receivers having noiseless conference links of finite capacities and between them .then , for sending a common message to both receivers , any rate must satisfy _  in also derived the following achievable rate for this scenario :  [ prop : achive_common_one_step ] _ ( ( * ? ? ? * theorem 5 ) ) _  _ assume the broadcast channel setup of proposition [ prop : common_upper ] .then , for sending a common message to both receivers , any rate satisfying _   , \nonumber\\       \label{eqn : prevresult1 }          r_{12}(p_x(x ) ) & \triangleq & \min \big ( i(x;y_1 ) + c_{21 } ,  \max\big\{i(x;y_2 ) ,             i(x;y_2 ) - h(y_1|y_2,x ) + \min\big(c_{12},h(y_1|y_2)\big)\big\ } \big),\phantom{xx}\\        \label{eqn : prevresult2 }          r_{21}(p_x(x ) ) & \triangleq & \min \big ( i(x;y_2 ) + c_{12 } ,             \max \big\{i(x;y_1 ) , i(x;y_1 )  - h(y_2|y_1,x ) + \min\big(c_{21},h(y_2|y_1)\big)\big\ } \big),\phantom{xx }       \end{aligned}\ ] ]  is achievable .note that this rate expression depends only on the parameters of the problem and is , therefore , computable . in proposition [ prop : achive_common_one_step ]the achievable rate increases linearly with the cooperation capacity .the downside of this method is that it produces a rate increase over the non - cooperative rate only for conference links capacities that exceed some minimum values .specializing the three independent messages result to the single common message case we obtain the following achievable rate with a -cycle conference for the general bc with a single common message :  [ corr : single - coomon - message - with - multi - step ] _ consider the general broadcast channel with cooperating receivers , having noiseless conference links of finite capacities and between them .let the receivers hold a conference that consists of cycles .then , any rate satisfying is achievable . _  here is defined as follows : } \min \left\ { r_1 , r_2 \right\},\ ] ] with    subject to    for the joint distribution the cardinality of the auxiliary random variables are bounded by :  is defined in a parallel manner to , with performing the first conference step , and the appropriate change in the probability chain .the proof of corollary [ corr : single - coomon - message - with - multi - step ] is provided in appendix [ appndx : prof_corollary_single_common ] .we note that ( * ? ? ?* theorem 2 ) presents a similar result for this scenario , under the constraint that the memoryless broadcast channel can be decomposed as , and considering the sum - rate of the conference .here we show that the same achievable rate expressions hold for the general memoryless broadcast channel .a recent result appears in , where the single common message case for a gaussian bc is considered . in the multi - cycle conference considered in this section ,we let the auxiliary rvs follow a more general chain than that of  which results in a larger achievable rate .consider the case where only a single cycle of conferencing between the receivers is allowed .specializing corollary [ corr : single - coomon - message - with - multi - step ] to a single cycle case we obtain    and the ts - eaf assignment is applying the ts - eaf assignment to and we obtain maximizing requires maximizing  ] , we obtain ^ * i(x;y_1|y_2)$ ] . combining with we have that the rate when decodes first is given by ^ * i(x;y_1|y_2)\right\},\ ] ] and by symmetric argumentwe can obtain .we conclude that the rate for the single - cycle conference with ts - eaf is given by ^ * i(x;y_1|y_2)\right\}\\   r_{21 } & = & \min \left\{i(x;y_1 ) + \left[\frac{c_{21}}{h(y_2|y_1)}\right]^ * i(x;y_2|y_1 ) , i(x;y_2 ) + c_{12}\right\}.\end{aligned}\ ] ] we note that this rate is always better than the point - to - point rate and also better than the joint - decoding rate of proposition [ prop : achive_common_one_step ] ( whenever cooperation can provide a rate increase ) .however , as in proposition [ prop : achive_common_one_step ] , at least one receiver has to satisfy the slepian - wolf condition for the full cooperation rate to be achieved .we also note that using ts - eaf with more than two steps does not improve upon this result .finally , we demonstrate the results of proposition [ prop : achive_common_one_step ] and corollary [ corr : single - coomon - message - with - multi - step ] through a symmetric bc example : consider the symmetric broadcast channel where and for any and .let .for this scenario we have that , in corollary [ corr : single - coomon - message - with - multi - step ] and also in proposition [ prop : achive_common_one_step ] .the resulting rate is depicted in figure [ fig : compare : ft_and_ts ] for a fixed probability .we can see that for this case , time - sharing exceeds joint - decoding for all values of .both methods meet the upper bound at .we note that this is a corrected version of the figure in .in this paper we considered the eaf technique using time - sharing on the auxiliary rvs . we first showed that incorporating joint - decoding at the destination into the eaf technique results in a special case of the classic eaf of ( * ? ? ? * theorem 6 ) .we then used the time - sharing assignment of the auxiliary rvs to obtain an easily computable achievable rate for the multiple - relay case , which can be compared against the daf - based results , to select the highest rate for any given scenario .next , we showed that for the gaussian relay channel with coded modulation , the gaussian auxiliary rv assignment is not always optimal , and a ts - eaf implementing a per - symbol hard decision may sometimes perform better .finally , we considered a third application of ts - eaf to the cooperative broadcast scenario with a multi - cycle conference .we first derived an achievable rate for the general channel , and then we specialized it to the single - cycle conference for which we obtained an explicit achievable rate .this rate is superior to the explicit expression that can be obtained with joint - decoding .in the final version .we evaluate , with given by and using :   1 .evaluating : note that both and are discrete rvs , therefore can be evaluated using the discrete entropies .the conditional distribution of given is given by : where  can be obtained from by switching and in .2 .  evaluating :write first and we note that using the chain rule we write  can be obtained by combining and which results in and we note that , since erasure is equivalent to no prior information. finally we note that by definition where next , we have using we obtain   next we need to evaluate :  1 . . here 2 .  by the definition of conditional entropy we have  , and for , for example , we have finally , we need to derive the distributions and . begin with and due to the symmetry , .we also have    we evaluate the achievable rate using .the distribution of is given by : and by symmetry , and .therefore , we need the conditional distribution : this allows us to evaluate . for evaluating note that and we need only to evaluate : by definition and note that .finally ,   evaluating we have : where ( a ) is due to the deterministic mapping from to , and can be evaluated using .   as we have that and converges in distribution to a bernoulli rv with probability .therefore where .now , letting we have that and therefore we conclude that as , then and therefore the becomes using the continuity of we conclude that for small values of , as decreases then is bounded from below .this implies that for small and small the feasibility is obtained only for large , which in turn implies low rate .we first write evaluating requires the marginal of . using the mapping defined in we find the marginal distribution of : where y_1\\   \pr(|y_1| < t ) &= & \int_{y_1 = -t}^{t } \frac{1}{2}\left[g_{y_1}(\sqrt{p},{\sigma_1 ^ 2})+ g_{y_1}(-\sqrt{p},{\sigma_1 ^ 2 } ) \right]d y_1.\end{aligned}\ ] ] also , due to symmetry we have that , and therefore we need only to find the conditional : and we note that .next , we need to evaluate .we first note that , we have we note that and that and are calculated exactly as in appendix [ sec : expressions_dhd ] for the dhd case .begin by writing where we used the fact that given , is independent of .all the terms in the above expressions have been calculated in the previous subsection , except :    here the relay uses the assignment of equation : we first evaluate   1 . 2 .we also have we need to evaluate where    using and we can write  where in ( a ) we used the fact that and are independent as , and that given , is independent of .in the following we highlight only the modifications from the general broadcast result due to the application of daf to the last conference step from to , and the fact that we transmit a single message .the transmitter generates codewords in an i.i.d .manner according to , . for transmission of the message at time the transmitter outputs .the conference steps from to are carried out exactly as in section [ sec : decencmultisteprgood ] .the first steps from to are carried out as in section [ sec : decencmultisteprbad ] . the conference step from to , is different from that of theorem [ thm : multi - step - general - bc ] , as after the step from to , may decode the message since received all the conference messages from .then , uses decode - and - forward for its conference transmission to .therefore , simply partitions into subsets in a uniform and independent manner .[ [ encoding - and - decoding - at - the - kth - conference - step - from - r_x2-to - r_x1 ] ] encoding and decoding at the conference step from to ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^  * before the conference step , decodes its message using his channel input and all the conference messages received from .this can be done with an arbitrarily small probability of error as long as is satisfied . *having decoded its message , uses the decode - and - forward strategy to select the conference message to .the conference capacity allocated to this step is . *having received the conference message from , can now decode its message using the information received at the first steps , and combining it with the information from the last step using the decode - and - forward decoding rule .this gives rise to .the bounds on , can be obtained as in section [ sec : combining_bounds_general ] : and similarly where is the total capacity allocated to the first conference steps from to .this provides the rate constraints on the conference auxiliary variables .

Abstract: _ in this work we focus on the general relay channel . we investigate the application of estimate - and - forward ( eaf ) to different scenarios . specifically , we consider assignments of the auxiliary random variables that always satisfy the feasibility constraints . we first consider the multiple relay channel and obtain an achievable rate without decoding at the relays . we demonstrate the benefits of this result via an explicit discrete memoryless multiple relay scenario where multi - relay eaf is superior to multi - relay decode - and - forward ( daf ) . we then consider the gaussian relay channel with coded modulation , where we show that a three - level quantization outperforms the gaussian quantization commonly used to evaluate the achievable rates in this scenario . finally we consider the cooperative general broadcast scenario with a multi - step conference . we apply estimate - and - forward to obtain a general multi - step achievable rate region . we then give an explicit assignment of the auxiliary random variables , and use this result to obtain an explicit expression for the single common message broadcast scenario with a two - step conference . _  ( 0,0 ) ( 0,70)submitted to the ieee transactions on information theory , october 2006 .


since the beginning of modern astronomy , the scientific community expressed a great interest in scientific visualisation tools .a strong boost in this direction was determined by the introduction of modern ccd detectors to collect observational data in a digital form .today , almost all the standard measures are digital and each measure can be generally considered as a collection of images forming a multi - dimensional data set . in many casesextensive image processing is required to obtain meaningful images .useful scientific information can be obtained from the raw data only using a data reduction pipeline .the most common data reduction tools , like iraf from national optical astronomy observatories ( noao ) and midas from european southern observatory , make an extensive use of visualization .this is supported by popular tools like avs , iris explorer , data visualizer and idl .however , these are generic purpose packages , not specifically designed for astrophysics .this makes often difficult their usage and they often required to learn a new specific programming language .furthermore it is usually hard , and some time impossible , to add user - developed data analysis tools .  besides observational data, the improvement of technology and the availability of super - computing multiprocessor system , have led to a dramatic increase of the volume of data coming from numerical simulations .astrophysical simulations produce today gigabytes of data which have to be efficiently visualized and analyzed .in fact a simulation produces several output to be correlated and analyzed , corresponding to different temporal tags and associated computational meshes ( sometimes irregular or structured grids ) .furthermore , particle methods ( n - body , sph , etc ) are , especially in cosmology , extremely popular . for this class of data the use of the above mentioned toolsis not adequate .specific tools , like tipsy , have been created and are commonly used .however , these tools are quite limited in their functionalities , can not describe and handle mesh - defined fields , usually associated to particles related quantities ( like mass ) , and are not designed to work efficiently with large amount of data .in this paper we present astromd , an analysis and visualization tool specifically designed to deal with the visualization and analysis of astrophysical data , avoiding or solving most of the previously described difficulties and limitations .astromd can manage different physical quantities .it can find structures having a not well defined shape or symmetries , and performs quantitative calculations on a selected region or structure .furthermore , it also makes use of virtual reality techniques which are particularly effective for understanding the three dimensional distribution of the fields , their geometry , topology or specific patterns .the display of data gives the illusion of a surrounding medium into which the user is immersed .the result is that the user has the impression of travelling through a computer - based multi - dimensional model which could be directly hand - manipulated . in this sense ,the virtual reality is a progressive lowering of the barrier which separates users from their data .astromd is developed by the visit ( visual information technology ) laboratory at cineca ( casalecchio di reno - bologna ) in collaboration with the astrophysical observatory of catania ( hereafter oact ) .astromd is an open source completely free code which is freely available ( see http://www.cineca.it/astromd ) .the plan of the paper is as follows . in section 2we will describe the basic features of astromd and the graphic user interface , in section 3 we describe the first test case on which astromd has been tested : the data produced in cosmological simulations performed using the parallel n - body tree code of the oact group .the preliminary results and data manipulation performed using astromd on these data are presented in section 4 . finally ,in section 5 , we draw the conclusions and future developments .data produced by astrophysical simulations have peculiarities that make them different from data produced with other kind of simulation or experiment .the principal features can be summarized as follows :   physical species have to be considered : for example , cosmological simulations consider both baryonic and dark matter .these two components have different physical properties and they have to be treated with different numerical approach .dark matter is usually described by n - body algorithms , while simulation carried out with baryons have a fluid - dynamical description ( either eulerian or lagrangian ) .further components , like stars or different chemical species , can be introduced and followed in a specific way .these kinds of data require different types of analysis and different kind of visualization techniques .dark matter needs the analysis of particle positions and velocity , while baryons require mesh based analysis and visualization .furthermore particle associated quantities , like the mass density or the gravitational potential , require their calculation and visualization on a mesh . structures in general have not a well defined shape or particular symmetries .furthermore they can be distributed with no regularity in the computational box .therefore it is necessary to have a clear 3d representation and efficient and fast tools of navigation , selection , zoom and the possibility of improving the resolution and the accuracy of calculations in specific user - selected regions   changes dynamically the properties of the simulated objects and the information that can be retrieved , therefore it is important to control efficiently sequences of time - frames .astromd is specifically designed to deal properly with all these requirements . in the following subsectionswe will describe in detail the basic features of the package , the visualization , the data analysis , the graphic user interface and the stereo - graphic capabilities .astromd is developed using the visualization toolkit ( vtk ) by kitware , a freely available software portable on several platforms which range from the pc to the most powerful visualization systems , with a good scalability .vtk is designed for 3d computer graphics , image processing , and visualization .it includes a c++ class library and several interpreted interface layers .vtk has been ported on nearly every unix - based platform ( irix , solaris , linux etc . ) and pc s ( windows nt and windows 98 ) .the design and implementation of the library has been strongly influenced by object - oriented principles .the graphics model in vtk is at a higher level of abstraction than rendering libraries like opengl or pex .this means it is much easier to create useful graphics and visualization applications . in vtk applicationscan be written directly in c++ , tcl , java , or python . using these languages it is possible to build powerful , fast and portable applications .vtk supports a wide variety of visualization algorithms including scalar , vector , tensor , texture , and volumetric methods and advanced modelling techniques .it supports stereo - graphic rendering and can be used for virtual reality visualization .furthermore , being easily extensible , vtk allows the user to build ad hoc implementation of specific data analysis modules .the input data format presently accepted by astromd is the common unformatted c standard .binary quantities ( e.g. vector components ) are written in a continuous sequence with no labels or other symbols in within .the same result can be obtained in fortran using direct access files .however several data input formats like tipsy and hdf will be soon integrated .astromd can use the full dynamic range of the data , in order to retain the highest accuracy in the analysis .data are visualized with respect to a box which can describe the whole computational mesh or just a fraction of it .a sub - box can be selected interactively inside the parent box with a different spatial resolution , so that the user can focus on the most interesting regions .boxes can be translated , rotated , zoomed in and out with respect to selected positions .colors and luminosities can be chosen freely by the user .images of different evolutionary stages can be combined in order to obtain a dynamic view of the behaviour of the system .the program allows one to treat both particles and fields related data .the distribution of the particles can be easily visualized by astromd using the particles positions , as shown in fig . 1 and fig. 2 . +  the user can choose to use a sample of the data , in order to get a faster and easier visualization .the opacity of the particles can be increased , so that low density regions are more easily detectable , or decreased , so that the details of the high density regions substructures are better visualized .different particles species ( e.g. dark matter and baryons ) can be visualized at the same time using different colours .other particle - related continuous quantities , like density fields or the gravitational field , can be calculated as typical grid based fields .  in general , fields have a discrete representation on the cells of a computational mesh .the values of a field on a cell can be interpreted as the average value of the field over that cell . in section 4we will show several complementary ways of visualizing a field : different colours are associated to the values of the analyzed field .further possibilities of visualizing the field are either using cutting planes where iso - value curves are drawn , or projecting the distribution on a plane , integrating the field along the line of sight orthogonal to the plane . this last representation ,that is closer to what actually comes from observations , will be soon included in the package .finally , different time frames can be shown in a sequence .when particles are used , their positions are linearly interpolated between two available key - frames .this technique engenders a graphic animation in real time , giving the impression of a continuous movement of particles , generally a randomized sample of the global data set .both the single images and the whole sequence of time - step can be saved in bitmap format .further output formats will be soon made available .there are several astromd built - in tools which allow an efficient manipulation and analysis of the data .the following functionalities are in progress and all of them will be integrated in version 1 of the package . * particles mass density *  the mass density field associated to the particle distribution is calculated distributing the mass of each particle over the computational mesh by a eight points cloud in cell smoothing algorithm . the computation can be done with the maximum accuracy using all the particles over a uniform high resolution mesh , but astromd allows the user to use only a sample of the whole set of particles , and the final result can be extrapolated to all particles of the simulation , reducing the cpu time consuming and the memory request .the smoothing of the masses can be performed generally using a coarse grid , that can be refined where high resolution is necessary .the same tool can be used to calculate other fields related to quantities possibly associated to the particles , like , for example , the thermal energy density field or the x - ray luminosity field .* gravitational field calculation *  considering the mass density defined over the computational mesh as above , the gravitational field can be calculated solving the poisson equation where is the gravitational potential , by a fourier transform procedure . the poisson equation is transformed in its momentum space image using a fft vtk built - in function .this reduces the equation to a much simpler algebraic operation where and are the fourier images of the potential and of the density and is the square module of the wavenumber .finally the potential is transformed to the physical space using an inverse fft . * fourier decomposition , power spectrum and correlation function *  the quantity is used to calculate the power spectrum of the matter distribution , which is defined as the average value of the square norm of : the power spectrum expresses the weight of each of the fourier components of the mass distribution between and which represent the inverse of the size of the computational mesh and the nyquist frequency .the power spectrum is a powerful measure of the statistical properties of the distribution , together with the associated correlation function , which is its fourier transform .the correlation function indicates the probability to find a particle at a distance from any other particle , and is usually used to analyze the clustering properties of a sample of discrete objects ( particle , galaxies , galaxy clusters . etc . )the astromd graphic user interface has been projected for a simple and useful setting of the visualization parameters . + the commands are located in two main sections : a set of four menu buttons on the top of the astromd window and two columns of commands on the left side ( fig .3 ) . in the following we describe in detail the most important displayed commands . +  [ [ menu - buttons . ] ] menu buttons .+ + + + + + + + + + + + +  the * file * button contains the command to load three types of data : it is possible to load data which can refer to the gas , dark matter and stellar components of a simulated system .the different types of particles can be displayed all together or separately , depending on the type of information the user wants to obtain .+ the * view * button allows the selection of a point of view of the visualized system . these choices ( being also reported in the column of the commands ) , integrate the possibility to rotate , scale and zoom into the domain of the visualized system , using the mouse . + with the * tools * button , the user can select several utilities .the _ interactor _ permits to give vtk commands interactively ; the _ pipeline _ shows the vtk pipeline , that is the network of filters which transform data into graphics primitives and creates the visualized objects .the _ opacity _ selection allows to choice the values of opacity for the components of the astrophysical system .a more accurate setting of the opacities can be performed using the _ actor properties _4 ) : for each visualized object , permits the user to regulate the intensity and colour of the _ ambient light _ ,i.e. the light reflected or scattered from other objects in the scene ; the _ diffuse light _ , which is the light reflected by the object taking into account the angle of incidence of the light onto the object itself , the _ specular light _ , representing direct reflection of a light source off a shiny object , the _ specular power _ which tells how the object reflects the incoming light and the _ opacity _ which regulates the transparency of the object : an opacity value of 0 produces the object to be completely transparent .+ the surface colours of the displayed objects are obtained interpolating across polygons . the buttons , _ flat _ , _ gourand _ and _ phong _ correspond to three different types of interpolation :they are related to the process of transformation from graphic primitives to the visualized objects .the background colour can be selected from a button in the * tools * menu , the combination of colours and lights of the objects can be saved and reloaded .+ with the * options * button the user can select the stereo - graphic modality of visualization , wide the rendering window up to full screen and save the window geometry for particular situations . +  [ [ command - column . ] ] command column .+ + + + + + + + + + + + + + +  the * zoom * and * view from * section of commands allow the regulation of the point of view of the objects while the * show / hide * section of buttons select the components of the simulated system that the user wants to visualize .the _ box _ , _ gas _ ,_ dark _ and _ stars _ have obvious meanings ; the _ contour _ button is referred to the visualization of iso - surfaces , the _ sampler _ activation permits the computation of the properties for a subset of particles , and the _ boundary _ button shows a periodic reproduction with one tenth of the total number of particles in the box including all the system .+ the user can choose the sample of the loaded particle type ( i.e. stars , dark matter and gas particles ) , the size of the visualization box and the starting time from which he wants to show the evolution of the simulation .+ the * density * entries control the visualization of the iso - surfaces .these are calculated on a grid whose resolution can be user - selectable . + to allow the user to investigate with more accuracy a subset of the visualized system it is possible to use a cubic _sampler_. if the sampler is selected ( * show / hide * menu ) , visualized in the scene and enabled ( * sampler * menu ) , all the computations are performed only inside the region of the sampler .+ astromd can also show the evolution in time of the simulated system over all the interval of time for which the data are available , performing interpolations at intermediate frames .the * evolve * section permit to fix the initial and final times of the evolution and the number of steps used for the evolution . during the evolution the updated time of evolutionis displayed in the _ time _ entry of the * cloud * section .+ finally snapshots of the images displayed can be created using the button _ take it _ in the * screenshot * menu .a subdirectory named _ screenshot _ is created ( if it does not exist ) and bitmap images ( progressively numbered ) are created .+ all the groups of commands can be changed and are applied using the corresponding _ update _ command , the _ update _ command at the end of the left column updates all the system as a whole .astromd can represent data using stereo - graphic visualization and display data in three dimensions with a stereo - scopic technique .the 3d stereo - scopic perception , is based on the different angles we see a near object due to the distance of the eyes .the combination of the two images determine the position of the object in space .this process is reproduced by stereo - graphic visualization devices .the visualization system displays the same image as it is seen from slightly different points of view and presents it separately to each eye .this is done by different methods .the most common is using shutter glasses ( made with liquid crystals ) that act so that each eye only sees the image intended .the final superposition of the two images gives the impression of a 3d scene where th user is full immersed .the stereo images can be created on different kind of displays : the screen of a pc , the virtual theatre , up to the cave environments or the head mounted displays  the stereo - graphic functionalities of astromd are developed in the virtual theatre of cineca . in this environmentwe can use two different kind of displays : a wide cylindric screen ( m , view angle ) and a projective desk ( m , 29.1 dpi ) .the visualization is controlled by a sgi onix2 infinite reality2 system with eight mips r10000 processors , 4 gbytes dram and three graphic pipes .stereo - graphic visualization gives a useful enhancement of common 2d rendering for many applications .for example , the perception of the three dimensional distribution of structures is much easier .specific geometric or topological features of the sample comes out clearly from the 3d immersive representation .furthermore , it is possible to analyze quantities not directly dependent on the position , visualizing their correlations as planes or surfaces .a typical example is the fundamental plane of elliptic galaxies , which relates three observable quantities like the half - light radius , the mean surface brightness and the central velocity dispersion of these systems .in this section we will show some preliminary result we obtain applying the astromd tool to the data obtained from a simulation of 16 millions of particles studying the formation and the evolution of the universe .the simulation has been performed using the n - body tree code of the oact group run on the cray t3e supercomputer of cineca , . in the following subsectionwe briefly describe the tree code based on the barnes - hut algorithm ( hereafter bh ) , and the cosmological model we use to obtain the multi - dimensional data set .large cosmic structure simulations have improved enormously over the past decade both in terms of mass and force resolution .state - of - the - art n - body codes hardly allow one to deal with a number of particle n .+ the cosmological n - body simulations aim at finding a solution to a set of general relativistic equations of motions describing the motions of particles ( e.g. the postulated _ dark matter _ particles ) in the universe .these equations can be written in the form :   where is the mass of a particle , is the gravitational constant , is the time - varying expansion parameter ( the scale factor of the universe ) , and are the gravitational potential and the local density respectively at comoving coordinate , and is the mean mass density of the universe .the bh tree algorithm is a procedure to compute the gravitational force through a hierarchical subdivision of the computational domain into a set of cubic nested regions that form an adaptive tree data structure . generally speaking ,the _ bodies _ evolve in time according to the laws of newtonian physics : where .+ the fundamental approximation of the tree codes consist in the approximation of the force component for the _ i _ body . considering a region the force component on_ i _ may be computed as :    where and is the center of mass of .+ the system dynamics involves the advancement of the trajectories of all particles , and this is carried out through a discrete integration of the trajectory of each particle .+ the code has been parallelized in order to be used on the cray t3e system using both hpf - craft and shmem libraries .   as a test case for the astromd tool we use the output of a simulation with 16.777.216 particles run on a cray - t3e 256 processor based machine at the cineca .the system evolves in a cubic region with size of 50mpc ( about km ) .the cold dark matter cosmological model was used , each particle having about solar masses . with this kind of cosmological modelit is possible to study the formation and the evolution of galaxies and clusters of galaxies .the simulation starts at a time ( red - shift ) , where the latter parameter is a standard measure of time adopted in cosmology .the age of the universe can be calculated from the red - shift parameter using the following equation : where , which is valid for the cosmological models we have simulated . at the age of the universe was about 24 million years , when the matter of the universe was still almost uniformly distributed .the simulation was stopped at the value , the actual age of the universe .the system evolve for about 270 time - steps using the opening parameter and clusters of galaxies start to form at about .we collected 22 output check point files starting from up to the end of the simulation totalling 18 gbytes of data ( position and velocity for each particle ) .this files were managed and randomized so that each selection of the first n particles in the output file , correspond to a selection of n random particles in the box where the system evolves . the astromd use this randomized files and the ancillary informations to visualize data and to extract the scientific informations as specified in the following paragraphs .1 shows a primordial distribution of dark matter particles inside the 50 mpc cubic region of the simulation above mentioned . in the displayed picture ,only a subset of 200,000 particles has been used , but owing to the fact that the data are randomized , a very good representation of the distribution of particles is obtained .this configuration is quite uniform , with small peaks of density .as it is well known , during the evolution the dark matter collapses onto these peaks of density leading to the formation of at least three main clusters of galaxies and several minor groups , embedded in a typical structure of voids and filaments ( fig .the system evolution , from the primordial distribution of matter up to the formation of the final structures , can be visualized by astromd .it is possible to note the augmentation of the velocity of collapse onto the proto - clusters and the oscillations of the matter density ( around the main peaks ) during the formation of the clusters . using the mouse it is possible to rotate the box and analyze the shapes of the clusters from different points of view ; moreover , zooming into the main structures , the details of the high density regions can be studied .a detailed analysis can be done setting a grid .5 shows the matter density field : the iso - surfaces are determined by connecting the cells in where the field has the same user - defined threshold value . in this figure the _ sampler _ has been used to show the iso - surfaces around the main cluster of galaxies in the simulation , fixing a value for the density 50 times greater than the mean background density , and using a grid of .the displayed iso - surface of the inner distribution of matter has the ellipsoidal shape . in fig .5 the iso - surfaces are completely opaque but lowering the opacity parameter value it is possible to see the particles of dark matter inside the iso - surface .+  another different way of visualizing the field is by a volume rendering technique , where the colour opacity is a function of the field and its value typically increase with the magnitude of the field itself .therefore , for example , low density regions appear more transparent ( and differently coloured ) than higher density ones .looking at the gas distribution in a cluster of galaxies , we can see through the outer shells , until the inner , more dense and more opaque core . in this way we mimic the actual behaviour of light through a dense medium .the enormous amount of data presently obtained both by observation and by numerical simulations , determines a growing request by astrophysicists of powerful tools which combine efficient visualization and accurate analysis capabilities .in this way both a qualitative and quantitative analysis of the data can be obtained and great benefits can be achieved .visualization , in fact , allows one to have a more intuitive approach to the data , to find out easily their overall properties and characteristics and to focus on the most interesting of them .data analysis gives the quantitative results required by the scientific analysis .we have presented astromd , a new data analysis and visualization tool , which should respond to this demand . in the preliminary versionwe have focused on the visualization aspects , with particular attention to 3d immersive rendering and on creating a friendly graphic user interface .this makes astromd a useful instrument already competitive with other existing software used in astronomy .the package is rapidly evolving and new functionalities , like a cluster identification and reconstruction algorithm , are being added .astromd has been built such that it is open source and portable on all the most common unix systems and ms windows .one of our basic purpose is to make it a wide spread product , highly diffused and used by the astrophysical community .the immersive virtual reality was tested using the virtual theatre immersive visualization facility made available from cineca .this is made up by : a graphic supercomputers , ( sgi onix2 infinite reality 2 , 8 processors r10000 , 4 gbytes ram ) ; a high resolution projection system ( 3 projectors barcographics ) ; a cylindric screen ( 2.7x9.1 m , 2816x768 pixels ) ; a projective desk ( 1.6x1.8 m , 29.6 dpi ) .we gratefully acknowledge useful discussion with dr .s. bassini , and we would like to thank g. erbacci of cineca for the useful help they gave us .

Abstract: over the past few years , the role of visualization for scientific purpose has grown up enormously . astronomy makes an extended use of visualization techniques to analyze data , and scientific visualization has became a fundamental part of modern researches in astronomy . with the evolution of high performance computers , numerical simulations have assumed a great role in the scientific investigation , allowing the user to run simulation with higher and higher resolution . data produced in these simulations are often multi - dimensional arrays with several physical quantities . these data are very hard to manage and to analyze efficiently . consequently the data analysis and visualization tools must follow the new requirements of the research . astromd is a tool for data analysis and visualization of astrophysical data and can manage different physical quantities and multi - dimensional data sets . the tool uses virtual reality techniques by which the user has the impression of travelling through a computer - based multi - dimensional model . astromd will be a freely available tool for the whole astronomical community .   _ keyword : _ n - body simulations , analysis tool , scientific visualization