Computation Over Gaussian Networks With Orthogonal Components

Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function. The arithmetic sum function in this paper is defined as a set of multiple weighted arithmetic sums, which includes averaging of the sources and estimating each of the sources as special cases. The type or frequency histogram function counts the number of occurrences of each argument, which yields many important statistics such as mean, variance, maximum, minimum, median, and so on. The proposed computation coding first abstracts Gaussian networks into the corresponding modulo sum multiple-access channels via nested lattice codes and linear network coding and then computes the desired function by using linear Slepian-Wolf source coding. For orthogonal Gaussian networks (with no broadcast and multiple-access components), the computation capacity is characterized for a class of networks. For Gaussian networks with multiple-access components (but no broadcast), an approximate computation capacity is characterized for a class of networks.Comment: 30 pages, 12 figures, submitted to IEEE Transactions on Information Theor

Multi-Way Relay Networks: Orthogonal Uplink, Source-Channel Separation and Code Design

We consider a multi-way relay network with an orthogonal uplink and correlated sources, and we characterise reliable communication (in the usual Shannon sense) with a single-letter expression. The characterisation is obtained using a joint source-channel random-coding argument, which is based on a combination of Wyner et al.'s "Cascaded Slepian-Wolf Source Coding" and Tuncel's "Slepian-Wolf Coding over Broadcast Channels". We prove a separation theorem for the special case of two nodes; that is, we show that a modular code architecture with separate source and channel coding functions is (asymptotically) optimal. Finally, we propose a practical coding scheme based on low-density parity-check codes, and we analyse its performance using multi-edge density evolution.Comment: Authors' final version (accepted and to appear in IEEE Transactions on Communications

Network Information Flow with Correlated Sources

In this paper, we consider a network communications problem in which multiple correlated sources must be delivered to a single data collector node, over a network of noisy independent point-to-point channels. We prove that perfect reconstruction of all the sources at the sink is possible if and only if, for all partitions of the network nodes into two subsets S and S^c such that the sink is always in S^c, we have that H(U_S|U_{S^c}) < \sum_{i\in S,j\in S^c} C_{ij}. Our main finding is that in this setup a general source/channel separation theorem holds, and that Shannon information behaves as a classical network flow, identical in nature to the flow of water in pipes. At first glance, it might seem surprising that separation holds in a fairly general network situation like the one we study. A closer look, however, reveals that the reason for this is that our model allows only for independent point-to-point channels between pairs of nodes, and not multiple-access and/or broadcast channels, for which separation is well known not to hold. This ``information as flow'' view provides an algorithmic interpretation for our results, among which perhaps the most important one is the optimality of implementing codes using a layered protocol stack.Comment: Final version, to appear in the IEEE Transactions on Information Theory -- contains (very) minor changes based on the last round of review

Orthogonal Multiple Access with Correlated Sources: Feasible Region and Pragmatic Schemes

In this paper, we consider orthogonal multiple access coding schemes, where correlated sources are encoded in a distributed fashion and transmitted, through additive white Gaussian noise (AWGN) channels, to an access point (AP). At the AP, component decoders, associated with the source encoders, iteratively exchange soft information by taking into account the source correlation. The first goal of this paper is to investigate the ultimate achievable performance limits in terms of a multi-dimensional feasible region in the space of channel parameters, deriving insights on the impact of the number of sources. The second goal is the design of pragmatic schemes, where the sources use "off-the-shelf" channel codes. In order to analyze the performance of given coding schemes, we propose an extrinsic information transfer (EXIT)-based approach, which allows to determine the corresponding multi-dimensional feasible regions. On the basis of the proposed analytical framework, the performance of pragmatic coded schemes, based on serially concatenated convolutional codes (SCCCs), is discussed

On Joint Source-Channel Coding for Correlated Sources Over Multiple-Access Relay Channels

We study the transmission of correlated sources over discrete memoryless (DM) multiple-access-relay channels (MARCs), in which both the relay and the destination have access to side information arbitrarily correlated with the sources. As the optimal transmission scheme is an open problem, in this work we propose a new joint source-channel coding scheme based on a novel combination of the correlation preserving mapping (CPM) technique with Slepian-Wolf (SW) source coding, and obtain the corresponding sufficient conditions. The proposed coding scheme is based on the decode-and-forward strategy, and utilizes CPM for encoding information simultaneously to the relay and the destination, whereas the cooperation information from the relay is encoded via SW source coding. It is shown that there are cases in which the new scheme strictly outperforms the schemes available in the literature. This is the first instance of a source-channel code that uses CPM for encoding information to two different nodes (relay and destination). In addition to sufficient conditions, we present three different sets of single-letter necessary conditions for reliable transmission of correlated sources over DM MARCs. The newly derived conditions are shown to be at least as tight as the previously known necessary conditions.Comment: Accepted to TI