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

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

Nested Lattice Codes for Gaussian Relay Networks with Interference

In this paper, a class of relay networks is considered. We assume that, at a node, outgoing channels to its neighbors are orthogonal, while incoming signals from neighbors can interfere with each other. We are interested in the multicast capacity of these networks. As a subclass, we first focus on Gaussian relay networks with interference and find an achievable rate using a lattice coding scheme. It is shown that there is a constant gap between our achievable rate and the information theoretic cut-set bound. This is similar to the recent result by Avestimehr, Diggavi, and Tse, who showed such an approximate characterization of the capacity of general Gaussian relay networks. However, our achievability uses a structured code instead of a random one. Using the same idea used in the Gaussian case, we also consider linear finite-field symmetric networks with interference and characterize the capacity using a linear coding scheme.Comment: 23 pages, 5 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

Source and Physical-Layer Network Coding for Correlated Two-Way Relaying

In this paper, we study a half-duplex two-way relay channel (TWRC) with correlated sources exchanging bidirectional information. In the case, when both sources have the knowledge of correlation statistics, a source compression with physical-layer network coding (SCPNC) scheme is proposed to perform the distributed compression at each source node. When only the relay has the knowledge of correlation statistics, we propose a relay compression with physical-layer network coding (RCPNC) scheme to compress the bidirectional messages at the relay. The closed-form block error rate (BLER) expressions of both schemes are derived and verified through simulations. It is shown that the proposed schemes achieve considerable improvements in both error performance and throughput compared with the conventional non-compression scheme in correlated two-way relay networks (CTWRNs).Comment: 15 pages, 6 figures. IET Communications, 201

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

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201

Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

Source-Channel Coding Theorems for the Multiple-Access Relay Channel

We study reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs). In MARCs only the destination is interested in reconstructing the sources, while in MABRCs both the relay and the destination want to reconstruct them. In addition to arbitrary correlation among the source signals at the users, both the relay and the destination have side information correlated with the source signals. Our objective is to determine whether a given pair of sources can be losslessly transmitted to the destination for a given number of channel symbols per source sample, defined as the source-channel rate. Sufficient conditions for reliable communication based on operational separation, as well as necessary conditions on the achievable source-channel rates are characterized. Since operational separation is generally not optimal for MARCs and MABRCs, sufficient conditions for reliable communication using joint source-channel coding schemes based on a combination of the correlation preserving mapping technique with Slepian-Wolf source coding are also derived. For correlated sources transmitted over fading Gaussian MARCs and MABRCs, we present conditions under which separation (i.e., separate and stand-alone source and channel codes) is optimal. This is the first time optimality of separation is proved for MARCs and MABRCs.Comment: Accepted to IEEE Transaction on Information Theor