Low-complexity approaches to distributed data dissemination

Abstract

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 145-153).In this thesis we consider practical ways of disseminating information from multiple senders to multiple receivers in an optimal or provably close-to-optimal fashion. The basis for our discussion of optimal transmission of information is mostly information theoretic - but the methods that we apply to do so in a low-complexity fashion draw from a number of different engineering disciplines. The three canonical multiple-input, multiple-output problems we focus our attention upon are: * The Slepian-Wolf problem where multiple correlated sources must be distributedly compressed and recovered with a common receiver. * The discrete memoryless multiple access problem where multiple senders communicate across a common channel to a single receiver. * The deterministic broadcast channel problem where multiple messages are sent from a common sender to multiple receivers through a deterministic medium. Chapter 1 serves as an introduction and provides models, definitions, and a discussion of barriers between theory and practice for the three canonical data dissemination problems we will discuss. Here we also discuss how these three problems are all in different senses 'dual' to each other, and use this as a motivating force to attack them with unifying themes.(cont.) Chapter 2 discusses the Slepian-Wolf problem of distributed near-lossless compression of correlated sources. Here we consider embedding any achievable rate in an M-source problem to a corner point in a 2M - 1-source problem. This allows us to employ practical iterative decoding techniques and achieve rates near the boundary with legitimate empirical performance. Both synthetic data and real correlated data from sensors at the International Space Station are used to successfully test our approach. Chapter 3 generalizes the investigation of practical and provably good decoding algorithms for multiterminal systems to the case where the statistical distribution of the memoryless system is unknown. It has been well-established in the theoretical literature that such 'universal' decoders exist and do not suffer a performance penalty, but their proposed structure is highly nonlinear and therefore believed to be complex. For this reason, most discussion of such decoders has been limited to the realm of ontology and proof of existence. By exploiting recently derived results in other engineering disciplines (i.e. expander graphs, linear programming relaxations, etc), we discuss a code construction and two decoding algorithms that have polynomial complexity and admit provably good performance (exponential error probability decay).(cont.) Because there is no need for a priori statistical knowledge in decoding (which in many settings - for instance a sensor network - might be difficult to repeatedly acquire without significant cost), this approach has very attractive robustness, energy efficiency, and stand-alone practical implications. Finally, Chapter 4 walks away from the multiple-sender, single-receiver setting and steps into the single-sender-multiple receiver setting. We focus our attention here on the deterministic broadcast channel, which is dual to the Slepian-Wolf and multiple access problems in a number of ways - including how the difficulty of practical implementation lies in the encoding rather than decoding. Here we illustrate how again a splitting approach can be applied, and how the same properties from the Slepian-Wolf and multiple access splitting settings remain. We also discuss practical coding strategies for some problems motivated by wireless, and show how by properly 'dualizing' provably good decoding strategies for some channel coding problems, we admit provably good encoding for this setting.by Todd Prentice Coleman.Ph.D