A new source-splitting approach to the Slepian-Wolf problem

It is shown that achieving an arbitrary rate-point in the achievable region of the M-source Slepian-Wolf [1] problem may be reduced via a practical source-splitting transformation to achieving a corner point in a 2M − 1 source Slepian-Wolf problem. Moreover, each source must be split at most once. This approach extends the ideas introduced in [2] to a practical setting: it does not require common randomness shared between splitters and the decoders, the cardinality of each source split is strictly smaller than the original, and practical iterative decoding methods can achieve rates near the theoretical bound

Low-Complexity Approaches to Slepian–Wolf Near-Lossless Distributed Data Compression

This paper discusses the Slepian–Wolf problem of distributed near-lossless compression of correlated sources. We introduce practical new tools for communicating at all rates in the achievable region. The technique employs a simple “source-splitting” strategy that does not require common sources of randomness at the encoders and decoders. This approach allows for pipelined encoding and decoding so that the system operates with the complexity of a single user encoder and decoder. Moreover, when this splitting approach is used in conjunction with iterative decoding methods, it produces a significant simplification of the decoding process. We demonstrate this approach for synthetically generated data. Finally, we consider the Slepian–Wolf problem when linear codes are used as syndrome-formers and consider a linear programming relaxation to maximum-likelihood (ML) sequence decoding. We note that the fractional vertices of the relaxed polytope compete with the optimal solution in a manner analogous to that observed when the “min-sum” iterative decoding algorithm is applied. This relaxation exhibits the ML-certificate property: if an integral solution is found, it is the ML solution. For symmetric binary joint distributions, we show that selecting easily constructable “expander”-style low-density parity check codes (LDPCs) as syndrome-formers admits a positive error exponent and therefore provably good performance

On some new approaches to practical Slepian-Wolf compression inspired by channel coding

This paper considers the problem, first introduced by Ahlswede and Körner in 1975, of lossless source coding with coded side information. Specifically, let X and Y be two random variables such that X is desired losslessly at the decoder while Y serves as side information. The random variables are encoded independently, and both descriptions are used by the decoder to reconstruct X. Ahlswede and Körner describe the achievable rate region in terms of an auxiliary random variable. This paper gives a partial solution for the optimal auxiliary random variable, thereby describing part of the rate region explicitly in terms of the distribution of X and Y

Rate-splitting for the deterministic broadcast channel

We show that the deterministic broadcast channel, where a single source transmits to M receivers across a deterministic mechanism, may be reduced, via a rate-splitting transformation, to another (2M−1)-receiver deterministic broadcast channel problem where a successive encoding approach suffices. Analogous to rate-splitting for the multiple access channel and source-splitting for the Slepian-Wolf problem, all achievable rates (including non-vertices) apply. This amounts to significant complexity reduction at the encoder

Time-sharing vs. source-splitting in the Slepian-Wolf problem: error exponents analysis

We discuss two approaches for decoding at arbitrary rates in the Slepian-Wolf problem - time sharing and source splitting - both of which rely on constituent vertex decoders. We consider the error exponents for both schemes and conclude that source-splitting is more robust at coding at arbitrary rates, as the error exponent for time-sharing degrades significantly at rates near vertices. As a by-product of our analysis, we exhibit an interesting connection between minimum mean-squared error estimation and error exponents

Successive Wyner-Ziv Coding Scheme and its Application to the Quadratic Gaussian CEO Problem

We introduce a distributed source coding scheme called successive Wyner-Ziv coding. We show that any point in the rate region of the quadratic Gaussian CEO problem can be achieved via the successive Wyner-Ziv coding. The concept of successive refinement in the single source coding is generalized to the distributed source coding scenario, which we refer to as distributed successive refinement. For the quadratic Gaussian CEO problem, we establish a necessary and sufficient condition for distributed successive refinement, where the successive Wyner-Ziv coding scheme plays an important role.Comment: 28 pages, submitted to the IEEE Transactions on Information Theor

Cores of Cooperative Games in Information Theory

Cores of cooperative games are ubiquitous in information theory, and arise most frequently in the characterization of fundamental limits in various scenarios involving multiple users. Examples include classical settings in network information theory such as Slepian-Wolf source coding and multiple access channels, classical settings in statistics such as robust hypothesis testing, and new settings at the intersection of networking and statistics such as distributed estimation problems for sensor networks. Cooperative game theory allows one to understand aspects of all of these problems from a fresh and unifying perspective that treats users as players in a game, sometimes leading to new insights. At the heart of these analyses are fundamental dualities that have been long studied in the context of cooperative games; for information theoretic purposes, these are dualities between information inequalities on the one hand and properties of rate, capacity or other resource allocation regions on the other.Comment: 12 pages, published at http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/318704 in EURASIP Journal on Wireless Communications and Networking, Special Issue on "Theory and Applications in Multiuser/Multiterminal Communications", April 200