Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decode-and-forward the source message to the destination, or they compress-and-forward their channel outputs to the destination. The decode-and-forward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compress-and-forward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination’s channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasi-static fading problems, cases where partial channel knowl-edge is available at the transmitters, and cases where local user co-operation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels.

What makes a source-channel communication system optimal? It is shown that in order to achieve an optimal cost--distortion tradeoff, the source and the channel have to be matched in a probabilistic sense. The match (or lack of it) involves the source distribution, the distortion measure, the channel conditional distribution, and the channel input cost function. Closed-form necessary and sufficient expressions relating the above entities are given. This generalizes both the separation-based approach as well as the two well-known examples of optimal uncoded communication. The condition of

The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cut-set arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cut-set upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source–channel coding problem, and it is well known that the source–channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance—it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include certain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source–destination pair, capacity grows with the logarithm of the number of nodes.

The problem of reliably reconstructing a function of sources over a multiple-access channel is considered. It is shown that there is no source-channel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separation-based strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multiple-access channel with a joint source-channel lattice code. Finally, computation codes are used to determine the multicast capacity of finite field multiple-access networks, thus linking them to network coding.

A discrete denoising algorithm estimates the input sequence to a discrete memoryless channel (DMC) based on the observation of the entire output sequence. For the case in which the DMC is known and the quality of the reconstruction is evaluated with a given single-letter fidelity criterion, we propose a discrete denoising algorithm that does not assume knowledge of statistical properties of the input sequence. Yet, the algorithm is universal in the sense of asymptotically performing as well as the optimum denoiser that knows the input sequence distribution, which is only assumed to be stationary and ergodic. Moreover, the algorithm is universal also in a semi-stochastic setting, in which the input is an individual sequence, and the randomness is due solely to the channel noise.

Sensors acquire data, and communicate this to an interested party. The arising coding problem is often split into two parts: First, the sensors compress their respective acquired signals, potentially applying the concepts of distributed source coding. Then, they communicate the compressed version to the interested party, the goal being not to make any errors. This coding paradigm is inspired by Shannon’s separation theorem for point-to-point communication, but it leads to suboptimal performance in general network topologies. The optimal performance for the general case is not known. In this paper, we propose an alternative coding paradigm based on joint source-channel coding. This coding paradigm permits to determine the optimal performance for a class of sensor networks, and shows how to achieve it. For sensor networks outside this class, we argue that the goal of the coding system could be to approach our condition for optimal performance as closely as possible. This is supported by examples for which our coding paradigm significantly outperforms the traditional separation-based coding paradigm. In particular, for a Gaussian example considered in this paper, the distortion of the best coding scheme according to the separation paradigm decreases like 1 / log M, while for our coding paradigm, it decreases like 1/M, where M is the total number of sensors.

Abstract — One of the simplest sensor network models has one single underlying Gaussian source of interest, observed by many sensors, subject to independent Gaussian observation noise. The sensors communicate over a standard Gaussian multipleaccess channel to a fusion center whose goal is to estimate the underlying source with respect to mean-squared error. In this note, a theorem of Witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission, i.e., each sensors ’ channel input is merely a scaled version of its noisy observation. I.

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a non-sparse representation. To capture efficiently these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multi-directional (M-DIR) and anisotropic transform is required. We present a new lattice-based perfect reconstruction and critically sampled anisotropic M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional (2-D) WT. The corresponding anisotropic basis functions (directionlets) have directional vanishing moments (DVM) along any two directions with rational slopes. Furthermore, we show that this novel transform provides an efficient tool for non-linear approximation (NLA) of images, achieving the approximation power O(N −1.55), which is competitive to the rates achieved by the other oversampled transform constructions.

This paper investigates reliable and unreliable forwarding strategies in a parallel-relay network. We consider the problem that maximizes the achievable rate under the total power constraint that allows for the power allocation among the nodes. We approach this problem by solving its dual with the objective to communicate to the destination at rate   using minimum transmitted power. Motivated by applications in sensor networks, we assume large bandwidth resources allowing orthogonal transmissions at the nodes. In such a network, the energy cost per information bit [1] during the reliable forwarding is minimized by operating in the wideband regime. For the wideband decodeand-forward (DF) strategy, we present the optimum parallel-relay solution by identifying the best choice of relay nodes and the optimum power allocation among them. We demonstrate that the data should be sent over a single relay route through one relay that is in the “best ” position in the network. On the other hand, as observed in [2], the benefit of unreliable amplify-and-forward (AF) strategy diminishes in the wideband regime. We characterize the optimum bandwidth for AF that minimizes the total energy cost per information bit for our network model. We show that transmitting in the optimum bandwidth allows the network to operate in the linear regime where the achieved rate increases linearly with transmit power. We then identify the best subset of AF relay nodes and characterize the optimum power allocation per dimension among relays, for a given source power and bandwidth. Based on this analysis, we compare the energy-efficiency of DF and AF in a one-relay network and show the regions where each strategy is optimal.

We study the power-versus-distortion trade-off for the transmission of a memoryless bivariate Gaussian source over a two-to-one Gaussian multiple-access channel with perfect causal feedback. In this problem, each of two separate transmitters observes a different component of a memoryless bivariate Gaussian source as well as the feedback from the channel output of the previous time-instants. Based on the observed source sequence and the feedback, each transmitter then describes its source component to the common receiver via an average-power constrained Gaussian multiple-access channel. From the resulting channel output, the receiver wishes to reconstruct both source components with the least possible expected squared-error distortion. We study the set of distortion pairs that can be achieved by the receiver on the two source components. We present sufficient conditions and necessary conditions for the achievability of a distortion pair. These conditions are expressed in terms of the source correlation and of the signal-to-noise ratio (SNR) of the channel. In several cases the necessary conditions and sufficient conditions coincide. This allows us to show that if the channel SNR is below a certain threshold, then an uncoded transmission scheme that ignores the feedback is optimal. Thus, below this SNR-threshold feedback is useless. We also derive the precise high-SNR asymptotics of optimal schemes. 1