The multiway relay channel is a multicast network where L users exchange data through a relay. In this paper, the capacity region of a class of multiway relay channels is derived, where the channel inputs and outputs take values over finite fields. The cut-set upper bound to the capacity region is derived and is shown to be achievable by our proposed functional-decode-forward coding strategy. More specifically, for the general case where the users can transmit at possibly different rates, functional-decode-forward, combined with rate splitting and joint source-channel decoding, is proved to achieve the capacity region; while for the case where all users transmit at a common rate, rate splitting and joint source-channel decoding are not required to achieve the capacity. That the capacity-achieving coding strategies do not utilize the users' received signals in the users' encoding functions implies that feedback does not increase the capacity region of this class of multiway relay channels.
The MWRC has also been studied from the point of view of source coding, where multiple users exchange possibly correlated data via a relay. In the source coding setting, the channel from the users to the relay and that from the relay to the users are assumed to be noiseless. The problem formulation is how many bits the users need to encode their respective messages to be sent to the relay; and after the relay receives these encoded messages, how many bits the relay needs to transmit to the users in order for each user to recover the messages of all other users. The three-user lossless case (where each user perfectly reconstructs the other two users' messages) was studied by Wyner @cite_18 , the two-user lossless case and lossy case (where each user reconstructs the other user's message with a prescribed distortion) was studied by Su and El Gamal @cite_28 , and the two-user lossy case with common reconstructions (where each user must also be able to determine the lossy reconstructed message of the other user) was studied by Timo @cite_12 .
@cite_28 @cite_18 @cite_12
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We study the transmission over a network in which users send information to a remote destination through relay nodes that are connected to the destination via finite-capacity error-free links, i.e., a cloud radio access network. The relays are constrained to operate without knowledge of the users' codebooks, i.e., they perform oblivious processing. The destination, or central processor, however, is informed about the users' codebooks. We establish a single-letter characterization of the capacity region of this model for a class of discrete memoryless channels in which the outputs at the relay nodes are independent given the users' inputs. We show that both relaying a-la Cover-El Gamal, i.e., compress-and-forward with joint decompression and decoding, and "noisy network coding", are optimal. The proof of the converse part establishes, and utilizes, connections with the Chief Executive Officer (CEO) source coding problem under logarithmic loss distortion measure. Extensions to general discrete memoryless channels are also investigated. In this case, we establish inner and outer bounds on the capacity region. For memoryless Gaussian channels within the studied class of channels, we characterize the capacity region when the users are constrained to time-share among Gaussian codebooks. Furthermore, we also discuss the suboptimality of separate decompression-decoding and the role of time-sharing. A 3-node lossy source coding problem for a 2-DMS (X 1 ,X 2 ) is considered. Source nodes 1 and 2 observe X 1 and X 2 , respectively, and each wishes to reconstruct the other source with a prescribed distortion. To achieve these goals, nodes 1 and 2 send descriptions of their sources to relay node 3. The relay node then broadcasts a joint description to the source nodes. A cutset outer bound and a compress-linear code inner bound are established and shown to coincide in several special cases. A compute-compress inner bound is then presented and shown to outperform the compress-linear code in some cases. An outer bound based on Kaspi's converse for the two-way source coding problem is shown to be strictly tighter than the cutset outer bound. In this paper, a point-to-point orthogonal-frequency- division multiplexing (OFDM) system with a decode-and- forward (DF) relay is considered. The transmission consists of two hops. The source transmits in the first hop, and the relay transmits in the second hop. Each hop occupies one time slot. The relay is half-duplex, and capable of decoding the message on a particular subcarrier in one time slot, and re-encoding and forwarding it on a different subcarrier in the next time slot. Thus, each message is transmitted on a pair of subcarriers in two hops. It is assumed that the destination is capable of combining the signals from the source and the relay pertaining to the same message. The goal is to maximize the weighted sum rate of the system by jointly optimizing subcarrier pairing and power allocation on each subcarrier in each hop. The weighting of the rates is to take into account the fact that different subcarriers may carry signals for different services. Both total and individual power constraints for the source and the relay are investigated. For the situations where the relay does not transmit on some subcarriers because doing so does not improve the weighted sum rate, we further allow the source to transmit new messages on these idle subcarriers. To the best of our knowledge, such a joint optimization inclusive of the destination combining has not been discussed in the literature. The problem is first formulated as a mixed integer programming problem. It is then transformed to a convex optimization problem by continuous relaxation, and solved in the dual domain. Based on the optimization results, algorithms to achieve feasible solutions are also proposed. Simulation results show that the proposed algorithms almost achieve the optimal weighted sum rate and outperform the existing methods in various channel conditions. The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multiway relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, such that the users within the same cluster wish to exchange messages among themselves, i.e., each user multicasts its message to all the other users in its own cluster. It is assumed that the users cannot receive each other's signals directly. Hence, the relay terminal in this model is the enabler of communication. In particular, restricted encoders are considered, such that the encoding function of each user depends only on its own message and the received signal is used only for decoding the messages of the other users in the cluster. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of the exchange rate, the symmetric rate point in the capacity region in a symmetric Gaussian mRC scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the optimal exchange rate, independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding-based achievable schemes, a nested lattice coding-based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity. In this paper, we investigate the transmission completion time minimization problem in an additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature, using a rechargeable battery. The harvested energy is modeled to arrive at the transmitter during the course of transmissions. The transmitter has a fixed number of packets to be delivered to each receiver. The objective is to minimize the time by which all of the packets are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates in a deterministic setting. We first analyze the structural properties of the optimal transmission policy in a two-user broadcast channel via the dual problem of maximizing the departure region by a fixed time T. We prove that the optimal total transmit power sequence has the same structure as the optimal single-user transmit power sequence in . In addition, the total power is split optimally based on a cut-off power level; if the total transmit power is lower than this cut-off level, all transmit power is allocated to the stronger user; otherwise, all transmit power above this level is allocated to the weaker user. We then extend our analysis to an M-user broadcast channel. We show that the optimal total power sequence has the same structure as the two-user case and optimally splitting the total power among M users involves M-1 cut-off power levels. Using this structure, we propose an algorithm that finds the globally optimal policy. Our algorithm is based on reducing the broadcast channel problem to a single-user problem as much as possible. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings. We study the application of convolutional codes to two-way relay networks (TWRNs) with physical-layer network coding (PNC). When a relay node decodes coded signals transmitted by two source nodes simultaneously, we show that the Viterbi algorithm (VA) can be used by approximating the maximum likelihood (ML) decoding for XORed messages as two-user decoding. In this setup, for given memory length constraint, the two source nodes can choose the same convolutional code that has the largest free distance in order to maximize the performance. Motivated from the fact that the relay node only needs to decode XORed messages, a low complexity decoding scheme is proposed using a reduced-state trellis. We show that the reduced-state decoding can achieve the same diversity gain as the full-state decoding for fading channels. Given two discrete memoryless channels (DMC's) with a common input, it is desired to transmit private messages to receiver 1 rate R_ 1 and common messages to both receivers at rate R_ o , while keeping receiver 2 as ignorant of the private messages as possible. Measuring ignorance by equivocation, a single-letter characterization is given of the achievable triples (R_ 1 ,R_ e ,R_ o ) where R_ e is the equivocation rate. Based on this channel coding result, the related source-channel matching problem is also settled. These results generalize those of Wyner on the wiretap channel and of Korner-Marton on the broadcast Channel. In this paper, we consider a three-terminal state-dependent relay channel (RC) with the channel state noncausally available at only the relay. Such a model may be useful for designing cooperative wireless networks with some terminals equipped with cognition capabilities, i.e., the relay in our setup. In the discrete memoryless (DM) case, we establish lower and upper bounds on channel capacity. The lower bound is obtained by a coding scheme at the relay that uses a combination of codeword splitting, Gel'fand-Pinsker binning, and decode-and-forward (DF) relaying. The upper bound improves upon that obtained by assuming that the channel state is available at the source, the relay, and the destination. For the Gaussian case, we also derive lower and upper bounds on the capacity. The lower bound is obtained by a coding scheme at the relay that uses a combination of codeword splitting, generalized dirty paper coding (DPC), and DF relaying; the upper bound is also better than that obtained by assuming that the channel state is available at the source, the relay, and the destination. In the case of degraded Gaussian channels, the lower bound meets with the upper bound for some special cases, and, so, the capacity is obtained for these cases. Furthermore, in the Gaussian case, we also extend the results to the case in which the relay operates in a half-duplex mode. We consider a state-dependent three-terminal full-duplex relay channel with the channel states noncausally available at only the source, that is, neither at the relay nor at the destination. This model has application to cooperation over certain wireless channels with asymmetric cognition capabilities and cognitive interference relay channels. We establish lower bounds on the channel capacity for both discrete memoryless (DM) and Gaussian cases. For the DM case, the coding scheme for the lower bound uses techniques of rate-splitting at the source, decode-and-forward (DF) relaying, and a Gel'fand-Pinsker-like binning scheme. In this coding scheme, the relay decodes only partially the information sent by the source. Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF. For the Gaussian case, we consider channel models in which each of the relay node and the destination node experiences on its link an additive Gaussian outside interference. We first focus on the case in which the links to the relay and to the destination are corrupted by the same interference; and then we focus on the case of independent interferences. We also discuss a model with correlated interferences. For each of the first two models, we establish a lower bound on the channel capacity. The coding schemes for the lower bounds use techniques of dirty paper coding or carbon copying onto dirty paper, interference reduction at the source and decode-and-forward relaying. The results reveal that, by opposition to carbon copying onto dirty paper and its root Costa's initial dirty paper coding (DPC), it may be beneficial in our setup that the informed source uses a part of its power to partially cancel the effect of the interference so that the uninformed relay benefits from this cancellation, and so the source benefits in turn. This paper investigates the impact of inter-user non-orthogonality and asynchronous communication on the information-outage probability performance of multi-user decode-and-forward (DF) cooperative diversity in a code-division multiple-access (CDMA) uplink. Each user in the proposed system transmits its own data towards the base station and also serves as a relay for other users. We assume full-duplex communication so that each user can transmit and receive simultaneously at the same frequency. Each user attempts to decode the messages of a plurality of other users and forwards the superposition of multiple re-encoded and re-spread messages. Our cooperative scheme employs a sub-optimum decorrelating receiver to suppress the multi-user interference at both the base station and the relay-side. We evaluate the information-outage probability performance of the proposed scheme in an underloaded, fully-loaded and overloaded CDMA uplink. We consider combining schemes at the base station where the source information is code combined with the relayed information, while the information from multiple relays is either code combined or diversity combined. Under the system parameters contemplated in this paper, diversity combining of the relayed information is nearly as good as code combining because of the associated probabilities of decoding at the relays. We then examine the effect of using practical modulation formats on the information-outage probability performance of the proposed DF multi-user sharing scheme under diversity combining. We see that the performance loss due to modulation constraints and the use of diversity combining instead of code combining is relatively small. Let X , Y , Z be zero-mean, jointly Gaussian random vectors of dimensions nx, ny, and nz, respectively. Let P be the set of random variables W such that W harr Y harr (X, Z) is a Markov string. We consider the following optimization problem: WisinP min I(Y; Z) subject to one of the following two possible constraints: 1) I(X; W|Z) ges RI, and 2) the mean squared error between X and Xcirc = E(X|W, Z) is less than d . The problem under the first kind of constraint is motivated by multiple-input multiple-output (MIMO) relay channels with an oblivious transmitter and a relay connected to the receiver through a dedicated link, while for the second case, it is motivated by source coding with decoder side information where the sensor observation is noisy. In both cases, we show that jointly Gaussian solutions are optimal. Moreover, explicit water filling interpretations are given for both cases, which suggest transform coding approaches performed in different transform domains, and that the optimal solution for one problem is, in general, suboptimal for the other. This paper deals with the problem of multicasting a set of discrete memoryless correlated sources (DMCS) over a cooperative relay network. Necessary conditions with cut-set interpretation are presented. A Joint source-Wyner-Ziv encoding sliding window decoding scheme is proposed, in which decoding at each receiver is done with respect to an ordered partition of other nodes. For each ordered partition a set of feasibility constraints is derived. Then, utilizing the submodular property of the entropy function and a novel geometrical approach, the results of different ordered partitions are consolidated, which lead to sufficient conditions for our problem. The proposed scheme achieves operational separation between source coding and channel coding. It is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks, namely, Aref network and finite-field deterministic network. Also, in Gaussian cooperative networks, it is shown that reliable transmission of all DMCS whose Slepian-Wolf region intersects the cut-set bound region within a constant number of bits, is feasible. In particular, all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two-way relay networks. The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system. We consider a multiuser two-way relay network where multiple pairs of users communicate with their preassigned partners, using a common intermediate relay node, in a two-phase communication scenario employing code division multiple access (CDMA). By taking advantage of the bidirectional communication structure, we first propose that each pair of partners share a common spreading signature and design a jointly demodulate-and-XOR forward (JD-XOR-F) relaying scheme, where all users transmit to the relay simultaneously followed by the relay broadcasting an estimate of the XORed symbol for each user pair. We derive the decision rules and the corresponding bit error rates (BERs) at the relay and at the users' receivers. We then investigate the joint power control and receiver optimization problem for each phase for this multiuser two-way relay network with JD-XOR-F relaying. We solve each optimization problem by constructing the iterative power control and receiver updates that converge to the corresponding unique optimum. Simulation results are presented to demonstrate the performance of the proposed multiuser two-way JD-XOR-F relaying scheme in conjunction with the joint power control and receiver optimization algorithms. Specifically, we observe significant power savings and user capacity improvement with the proposed communication scheme as compared to the designs with a "one-way" communication perspective. We propose and design a practical modulation-coded (MC) physical-layer network coding (PNC) scheme to approach the capacity limits of Gaussian and fading two-way relay channels (TWRCs). In the proposed scheme, an irregular repeat–accumulate (IRA) MC over @math with the same random coset is employed at two users, which directly maps the message sequences into coded PAM or QAM symbol sequences. The relay chooses appropriate network coding coefficients and computes the associated finite-field linear combinations of the two users' message sequences using an iterative belief propagation algorithm. For a symmetric Gaussian TWRC, we show that, by introducing the same random coset vector at the two users and a time-varying accumulator in the IRA code, the MC-PNC scheme exhibits symmetry and permutation-invariant properties for the soft information distribution of the network-coded message sequence (NCMS). We explore these properties in analyzing the convergence behavior of the scheme and optimizing the MC to approach the capacity limit of a TWRC. For a block fading TWRC, we present a new MC linear PNC scheme and an algorithm used at the relay for computing the NCMS. We demonstrate that our developed schemes achieve near-capacity performance in both Gaussian and Rayleigh fading TWRCs. For example, our designed codes over GF(7) and GF(3) with a code rate of 3 4 are within 1 and 1.2 dB of the TWRC capacity, respectively. Our method can be regarded as a practical embodiment of the notion of compute-and-forward with a good nested lattice code, and it can be applied to a wide range of network configurations. The use of multi-user detection (MUD) in a cooperative CDMA network is investigated for the uplink in synchronous CDMA systems. Suppose that, at any instant in time, part of the users serve as sources while the others serve as relays. The proposed MUD scheme decorrelates the sources' messages at the destination with the help of precoding at the relays. Three cooperation methods are considered: (1) transmit beamforming, (2) selective relaying and (3) distributed space- time coding. The optimal weighting factors of each method are determined by taking the quality of the source-to-relay and or the relay-to-destination links into account. We show that significant improvements in terms of the spatial diversity and multiple-access interference (MAI) mitigation can be attained when precoding is employed at the relays to aid the decorrelation at the destination. The advantages are even more pronounced when selective relaying is combined with the other two schemes. We consider a dense fading multi-user network with multiple active multi-antenna source-destination pair terminals communicating simultaneously through a large common set of K multi-antenna relay terminals in the full spatial multiplexing mode. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) in meaningful asymptotic regimes of signal-to-noise ratio (SNR) and network size. We design linear distributed multi-antenna relay beamforming (LDMRB) schemes that exploit the spatial signature of multi-user interference and characterize their power-bandwidth tradeoff under a system-wide power constraint on source and relay transmissions. The impact of multiple users, multiple relays and multiple antennas on the key performance measures of the high and low SNR regimes is investigated in order to shed new light on the possible reduction in power and bandwidth requirements through the usage of such practical relay cooperation techniques. Our results indicate that point-to-point coded multi-user networks supported by distributed relay beamforming techniques yield enhanced energy efficiency and spectral efficiency, and with appropriate signaling and sufficient antenna degrees of freedom, can achieve asymptotically optimal power-bandwidth tradeoff with the best possible (i.e., as in the cutset bound) energy scaling of K-1 and the best possible spectral efficiency slope at any SNR for large number of relay terminals. Furthermore, our results help to identify the role of interference cancellation capability at the relay terminals on realizing the optimal power- bandwidth tradeoff; and show how relaying schemes that do not attempt to mitigate multi-user interference, despite their optimal capacity scaling performance, could yield a poor power- bandwidth tradeoff. In this paper, collocated and distributed space-time block codes (DSTBCs) which admit multi-group maximum likelihood (ML) decoding are studied. First the collocated case is considered and the problem of constructing space-time block codes (STBCs) which optimally tradeoff rate and ML decoding complexity is posed. Recently, sufficient conditions for multi-group ML decodability have been provided in the literature and codes meeting these sufficient conditions were called Clifford Unitary Weight (CUW) STBCs. An algebraic framework based on extended Clifford algebras is proposed to study CUW STBCs and using this framework, the optimal tradeoff between rate and ML decoding complexity of CUW STBCs is obtained for few specific cases. Code constructions meeting this tradeoff optimally are also provided. The paper then focuses on multi-group ML decodable DSTBCs for application in synchronous wireless relay networks and three constructions of four-group ML decodable DSTBCs are provided. Finally, the OFDM based Alamouti space-time coded scheme proposed by Li-Xia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Four-group decodable DSTBCs applicable in the proposed OFDM based transmission scheme are also given. We consider a multiuser two-way relay network where multiple pairs of users communicate with their pre-assigned partners, using a common intermediate relay node, in a two-phase communication scenario. In this system, a pair of partners transmit to the relay sharing a common spreading signature in the first phase, and the relay broadcasts an estimate of the XORed symbol for each user pair in the second phase employing the relaying scheme termed jointly demodulate-and-XOR forward (JD-XOR-F) in [1]. We investigate the joint power control and receiver optimization problem for this multiuser two-way relay system with JD-XOR-F relaying. We show that the total power optimization problem decouples into two subproblems, one for each phase. We construct the distributed power control and receiver updates in each phase which converge to the corresponding unique optimum. Simulation results are presented to demonstrate the significant power savings of the multiuser two-way relay system with the proposed iterative power control and receiver optimization algorithms, as compared to the designs with a iquestone-wayiquest communication perspective. We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in an M-user AWGN broadcast channel where the transmitter is able to harvest energy from the nature, using a finite storage capacity rechargeable battery. The harvested energy is modeled to arrive (be harvested) at the transmitter during the course of transmissions at arbitrary time instants. The transmitter has fixed number of packets for each receiver. Due to the finite battery capacity, energy may overflow without being utilized for data transmission. We derive the optimal offline transmission policy that minimizes the time by which all of the data packets are delivered to their respective destinations. We analyze the structural properties of the optimal transmission policy using a dual problem. We find the optimal total transmit power sequence by a directional water-filling algorithm. We prove that there exist M-1 cut-off power levels such that user i is allocated the power between the i-1st and the ith cut-off power levels subject to the availability of the allocated total power level. Based on these properties, we propose an algorithm that gives the globally optimal offline policy. The proposed algorithm uses directional water-filling repetitively. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings.