In this paper, we first consider a channel that is contaminated by two independent Gaussian noises @math and @math . The capacity of this channel is computed when independent noisy versions of @math are known to the transmitter and or receiver. It is shown that the channel capacity is greater then the capacity when @math is completely unknown, but is less then the capacity when @math is perfectly known at the transmitter or receiver. For example, if there is one noisy version of @math known at the transmitter only, the capacity is @math , where @math is the input power constraint and @math is the power of the noise corrupting @math . We then consider a Gaussian cognitive interference channel (IC) and propose a causal noisy dirty paper coding (DPC) strategy. We compute the achievable region using this noisy DPC strategy and quantify the regions when it achieves the upper bound on the rate.
Following Costa's work, several extensions of DPC have been studied, , colored Gaussian noise @cite_2 , arbitrary distributions of @math @cite_8 and deterministic sequences @cite_5 . The case when @math is perfectly known to the encoder and a noisy version is known to the decoder is considered in @cite_9 , mainly focusing on discrete memoryless channels. The only result in @cite_9 for Gaussian channel reveals no additional gain due to the presence of the noisy estimate at the decoder, since perfect knowledge is available at the encoder and DPC can be used. In contrast, in this paper we study the case when only noisy knowledge of @math is available at both transmitter and receiver.
@cite_8 @cite_5 @cite_9 @cite_2
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The sum capacity of a Gaussian broadcast MIMO channel can be achieved with dirty paper coding (DPC). However, algorithms that approach the DPC sum capacity do not appear viable in the forseeable future, which motivates lower complexity interference suppression techniques. Block diagonalization (BD) is a linear preceding technique for downlink multiuser MIMO systems. With perfect channel knowledge at the transmitter, BD can eliminate other users' interference at each receiver. In this paper, we study the sum capacity of BD with and without receive antenna selection. We analytically compare BD without receive antenna selection to DPC for a set of given channels. It is shown that (1) if the user channels are orthogonal to each other, then BD achieves the same sum capacity as DPC; (2) if the user channels lie in the same subspace, then the gain of DPC over BD can be upper bounded by the minimum of the number of transmit and receive antennas. These observations also hold for BD with receive antenna selection. Further, we study the ergodic sum capacity of BD with and without receive antenna selection in a Rayleigh fading channel. Simulations show that BD can achieve a significant part of the total throughput of DPC. An upper bound on the ergodic sum capacity gain of DPC over BD is proposed for easy estimation of the gap between the sum capacity of DPC and BD without receive antenna selection. 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. 1Consider an additive Gaussian noise channel affected by an additive interference sequence, taken from a given codebook, which is known non-causally at the transmitter (e.g., via prior decoding). It is known that in this case optimal performance is attained by Dirty Paper Coding, which treats the interference signal as unstructured. In other words, for this example, the knowledge of the specific interferer's codebook at the decoder is not useful in terms of capacity. In this paper, two variations of this basic scenario are presented in which treating interference as unstructured is instead generally suboptimal. In the first case, a second encoder of the source message is present in the system that is not aware of the interferer's sequence, and source and interference messages are uncorrelated; In the second case, the sources encoded by the informed transmitter and interferer are correlated (and an uninformed encoder may or may not be present). Results are given in terms of conditions for achievability for both discrete and Gaussian models of the scenarios discussed above, and corroborated by numerical results. Optimal strategies are also identified in special cases. The conclusions herein point to the importance of exploiting the interfererence structure in multiterminal and source-channel coding scenarios. Over discrete memoryless channels (DMC), linear decoders (maximizing additive metrics) afford several nice properties. In particular, if suitable encoders are employed, the use of decoding algorithms with manageable complexities is permitted. For a compound DMC, decoders that perform well without the channel's knowledge are required in order to achieve capacity. Several such decoders have been studied in the literature, however, there is no such known decoder which is linear. Hence, the problem of finding linear decoders achieving capacity for compound DMC is addressed, and it is shown that under minor concessions, such decoders exist and can be constructed. A geometric method based on the very noisy transformation is developed and used to solve this problem. Motivated by the error behavior in the DNA storage channel, in this paper, we extend the previously studied sequence reconstruction problem by Levenshtein. The reconstruction problem studies the model in which the information is read through multiple noisy channels, and the decoder, which receives all channel estimations, is required to decode the information. For the combinatorial setup, the assumption is that all the channels cause at most some @math errors. Levenshtein considered the case in which all the channels have the same behavior, and we generalize this model and assume that the channels are not identical. Thus, different channels may cause different maximum numbers of errors. For example, we assume that there are @math channels, which cause at most @math or @math errors, where @math t_ 1 @math pN @math 0 . If the information codeword belongs to a code with minimum distance @math , the problem is then to find the minimum number of channels that guarantees successful decoding in the worst case. A different problem we study in this paper is where the number of channels is fixed, and the question is finding the minimum distance @math that provides exact reconstruction. We study these problems and show how to apply them for the cases of substitutions and transpositions. This paper studies the zero-delay source-channel coding problem, and specifically the problem of obtaining the vector transformations that optimally map between the m-dimensional source space and k-dimensional channel space, under a given transmission power constraint and for the mean square error distortion. The functional properties of the cost are studied and the necessary conditions for the optimality of the encoder and decoder mappings are derived. An optimization algorithm that imposes these conditions iteratively, in conjunction with the noisy channel relaxation method to mitigate poor local minima, is proposed. The numerical results show strict improvement over prior methods. The numerical approach is extended to the scenario of source-channel coding with decoder side information. The resulting encoding mappings are shown to be continuous relatives of, and in fact subsume as special case, the Wyner-Ziv mappings encountered in digital distributed source coding systems. A well-known result in information theory pertains to the linearity of optimal encoding and decoding mappings in the scalar Gaussian source and channel setting, at all channel signal-to-noise ratios (CSNRs). In this paper, the linearity of optimal coding, beyond the Gaussian source and channel, is considered and the necessary and sufficient condition for linearity of optimal mappings, given a noise (or source) distribution, and a specified a total power constraint are derived. It is shown that the Gaussian source-channel pair is unique in the sense that it is the only source-channel pair for which the optimal mappings are linear at more than one CSNR values. Moreover, the asymptotic linearity of optimal mappings is shown for low CSNR if the channel is Gaussian regardless of the source and, at the other extreme, for high CSNR if the source is Gaussian, regardless of the channel. The extension to the vector settings is also considered where besides the conditions inherited from the scalar case, additional constraints must be satisfied to ensure linearity of the optimal mappings. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j<i is taken into account by coding for noncausally known interference. Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR). We conclude by providing some numerical results for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading. We study the discrete memoryless Z-interference channel where the transmitter of the pair that suffers from interference is cognitive. We first provide an outer bound on the capacity region of this channel. We then show that, when the channel of the transmitter-receiver pair that does not experience interference is deterministic and invertible, our proposed outer bound matches the best known inner bound. The obtained results imply that in the considered channel, superposition encoding at the noncognitive transmitter as well as Gel'fand-Pinsker encoding at the cognitive transmitter is needed in order to minimize the impact of interference. As a byproduct of the obtained capacity region, we obtain the capacity under the generalized Gel'fand-Pinsker setting where a transmitter-receiver pair communicates in the presence of interference noncausally known at the encoder. 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. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . This paper examines the problems of dirty-paper and dirty-tape coding with some additional side information (SI) at the decoder. In particular we focus on the situation in which the decoder SI is a noisy version of the SI at the encoder. We show that noisy SI at the decoder is advantageous for many channels in terms of capacity and, in general, the optimal coding strategy needs to take it into account. In particular, the capacities of the binary dirty-paper and dirty-tape channels are computed when the decoder SI is modeled as the output of a binary symmetric channel with the encoder SI as input. Moreover, the advantage offered by the decoder SI on the minimum achievable Eb NO in the dirty-tape scenario with Gaussian interference is demonstrated In this paper, we consider a discrete memoryless state-dependent relay channel with non-causal Channel State Information (CSI). We investigate three different cases in which perfect channel states can be known non-causally: i) only to the source, ii) only to the relay or iii) both to the source and to the relay node. For these three cases we establish lower bounds on the channel capacity (achievable rates) based on using Gel'fand-Pinsker coding at the nodes where the CSI is available and using Compress-and-Forward (CF) strategy at the relay. Furthermore, for the general Gaussian relay channel with additive independent and identically distributed (i.i.d) states and noise, we obtain lower bounds on the capacity for the cases in which CSI is available at the source or at the relay. We also compare our derived bounds with the previously obtained results which were based on Decode-and-Forward (DF) strategy, and we show the cases in which our derived lower bounds outperform DF based bounds, and can achieve the rates close to the upper bound. We consider a state-dependent multiaccess channel (MAC) with state noncausally known to some encoders. For simplicity of exposition, we focus on a two-encoder model in which one of the encoders has noncausal access to the channel state. The results can in principle be extended to any number of encoders with a subset of them being informed. We derive an inner bound for the capacity region in the general discrete memoryless case and specialize to a binary noiseless case. In binary noiseless case, we compare the inner bounds with trivial outer bounds obtained by providing the channel state to the decoder. In the case of maximum entropy channel state, we obtain the capacity region for binary noiseless MAC with one informed encoder. For a Gaussian state-dependent MAC with one encoder being informed of the channel state, we present an inner bound by applying a slightly generalized dirty paper coding (GDPC) at the informed encoder and a trivial outer bound by providing channel state to the decoder also. In particular, if the channel input is negatively correlated with the channel state in the random coding distribution, then GDPC can be interpreted as partial state cancellation followed by standard dirty paper coding. The uninformed encoders benefit from the state cancellation in terms of achievable rates, however, it seems that GDPC cannot completely eliminate the effect of the channel state on the achievable rate region, in contrast to the case of all encoders being informed. In the case of infinite state variance, we provide an inner bound and also provide a nontrivial outer bound for this case which is better than the trivial outer bound. 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. Writing on dirty paper, a variation of the standard additive white Gaussian noise (AWGN) channel with the channel output is considered. The Gaussian noise noncausally known at the transmitter does not affect the capacity of the AWGN channel. This is known as WDP property. The WDP property for three Gaussian multiple user channels with known capacity region is established. The achievable rate regions of corresponding discrete channels is proved. Although those regions may be suboptimal in general, they turn out to be optimal for these Gaussian channels. Alternative proofs can be obtained by successive uses of Costa's WDP coding scheme, from which the WDP property can be established for more general noise and state distributions. We study the degrees of freedom (DoF) of the @math -user interference channel with coordinated multipoint (CoMP) transmission and reception. Each message is jointly transmitted by @math successive transmitters, and is jointly received by @math successive receivers. We refer to this channel as the CoMP channel with a transmit cooperation order of @math and receive cooperation order of @math . Since the channel has a total of @math transmit antennas and @math receive antennas, the maximum possible DoF is equal to @math . We show that the CoMP channel has @math DoF if and only if @math . The key idea is that the zero forcing of the interference corresponding to the @math message at the decoder of the @math message, where @math , can be viewed as a shared responsibility between the @math transmitters carrying the @math message, and the @math receivers decoding the @math message. For the general case, we derive an outer bound that states that the DoF is bounded above by @math . For the special case with only CoMP transmission, i.e, @math , we propose a scheme that can achieve @math DoF for all @math K @math M_ t @math M_ t -1$ receivers, thereby allowing each of these receivers to enjoy 1 DoF, and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space. The achievability proofs are based on the notion of algebraic independence from algebraic geometry. Interference alignment has emerged as a powerful tool in the analysis of multiuser networks. Despite considerable recent progress, the capacity region of the Gaussian @math -user interference channel is still unknown in general, in part due to the challenges associated with alignment on the signal scale using lattice codes. This paper develops a new framework for lattice interference alignment, based on the compute-and-forward approach. Within this framework, each receiver decodes by first recovering two or more linear combinations of the transmitted codewords with integer-valued coefficients and then solving these linear combinations for its desired codeword. For the special case of symmetric channel gains, this framework is used to derive the approximate sum capacity of the Gaussian interference channel, up to an explicitly defined outage set of the channel gains. The key contributions are the capacity lower bounds for the weak through strong interference regimes, where each receiver should jointly decode its own codeword along with part of the interfering codewords. As part of the analysis, it is shown that decoding @math linear combinations of the codewords can approach the sum capacity of the @math -user Gaussian multiple-access channel up to a gap of no more than @math bits. This paper considers recovering @math -dimensional vectors @math , and @math from their circular convolutions @math . The vector @math is assumed to be @math -sparse in a known basis that is spread out in the Fourier domain, and each input @math is a member of a known @math -dimensional random subspace. We prove that whenever @math , the problem can be solved effectively by using only the nuclear-norm minimization as the convex relaxation, as long as the inputs are sufficiently diverse and obey @math . By “diverse inputs,” we mean that the @math ’s belong to different, generic subspaces. To the best of our knowledge, this is the first theoretical result on blind deconvolution where the subspace to which @math belongs is not fixed but needs to be determined. We discuss the result in the context of multipath channel estimation in wireless communications. Both the fading coefficients and the delays in the channel impulse response @math are unknown. The encoder codes the @math -dimensional message vectors randomly and then transmits coded messages @math ’s over a fixed channel one after the other. The decoder then discovers all of the messages and the channel response when the number of samples taken for each received message are roughly greater than @math , and the number of messages is roughly at least @math . The linear deterministic interference channel (LD-IC) with partial feedback is considered. Partial feedback for the LD-IC models a scenario in which the top l most-significant-bits of the channel output of receiver j are received as feedback at transmitter j, for j = 1, 2. The rationale for studying the LD-IC with partial feedback comes from the fact that it is a good approximation to the Gaussian interference channel with output feedback corrupted by additive white Gaussian noise (commonly referred to as noisy feedback). The main contribution of this paper is to characterize the capacity region of the symmetric LD-IC with partial feedback. The main ingredient of the proof is to obtain novel upper bounds on weighted rates 2R 1 + R 2 and R 1 + 2R 2 .