Algebraic Structures for Multi-Terminal Communication Systems.

We study a distributed source coding problem with multiple encoders, a central decoder and a joint distortion criterion. The encoders do not communicate with each other. The encoders observe correlated sources which they quantize and communicate noiselessly to a central decoder which is interested in minimizing a joint distortion criterion that depends on the sources and the reconstruction. We are interested in characterizing an inner bound to the optimal rate-distortion region. We first consider a special case where the sources are jointly Gaussian and the decoder wants to reconstruct a linear function of the sources under mean square error distortion. We demonstrate a coding scheme involving nested lattice codes that reconstructs the linear function by encoding in such a fashion that the decoder is able to reconstruct the function directly. For certain source distributions, this approach yields a larger rate-distortion region compared to when the decoder reconstructs lossy versions of the sources first and then estimates the function from them. We then extend this approach to the case of reconstructing a linear function of an arbitrary number of jointly Gaussian sources. Next, we consider the general distributed source coding problem with discrete sources. This formulation includes as a special case many famous distributed source coding problems. We present a new achievable rate-distortion region for this problem based on “good” structured nested random codes built over abelian groups. We demonstrate rate gains for this problem over traditional coding schemes using unstructured random codes. For certain sources and distortion functions, the new rate region is strictly bigger than the Berger-Tung rate region, which has been the best known achievable rate region for the problem till now. Further, there is no known way of achieving these rate gains without exploiting the structure of the coding scheme. Achievable performance limits for single-user source coding using abelian group codes are also obtained as corollaries of the main coding theorem. Our results also imply that nested linear codes achieve the Shannon rate-distortion bound in the single-user setting. Finally, we conclude by outlining some future research directions.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75917/1/dineshk_1.pd

On Causal Video Coding with Possible Loss of the First Encoded Frame

Multiple Description Coding (MDC) was fi rst formulated by A. Gersho and H. Witsenhausen as a way to improve the robustness of telephony links to outages. Lots of studies have been done in this area up to now. Another application of MDC is the transmission of an image in diff erent descriptions. If because of the link outage during transmission, any one of the descriptions fails, the image could still be reconstructed with some quality at the decoder side. In video coding, inter prediction is a way to reduce temporal redundancy. From an information theoretical point of view, one can model inter prediction with Causal Video Coding (CVC). If because of link outage, we lose any I-frame, how can we reconstruct the corresponding P- or B-frames at the decoder? In this thesis, we are interested in answering this question and we call this scenario as causal video coding with possible loss of the fi rst encoded frame and we denote it by CVC-PL as PL stands for possible loss. In this thesis for the fi rst time, CVC-PL is investigated. Although, due to lack of time, we mostly study two-frame CVC-PL, we extend the problem to M-frame CVC-PL as well. To provide more insight into two-frame CVC-PL, we derive an outer-bound to the achievable rate-distortion sets to show that CVC-PL is a subset of the region combining CVC and peer-to-peer coding. In addition, we propose and prove a new achievable region to highlight the fact that two-frame CVC-PL could be viewed as MDC followed by CVC. Afterwards, we present the main theorem of this thesis, which is the minimum total rate of CVC-PL with two jointly Gaussian distributed sources, i.e. X1 and X2 with normalized correlation coeffi cient r, for di fferent distortion pro files (D1,D2,D3). Defi ning Dr = r^2(D1 -1) + 1, we show that for small D3, i.e. D3 < Dr +D2 -1, CVC-PL could be treated as CVC with two jointly Gaussian distributed sources; for large D3, i.e. D3 > DrD2/(Dr+D2-DrD2), CVC-PL could be treated as two parallel peer-to-peer networks with distortion constraints D1 and D2; and for the other cases of D3, the minimum total rate is 0.5 log (1+ λ)(D3+λ)/ (Dr+λ )(D2+λ ) + 0.5 log Dr/(D1D3) where λ=D3-DrD2+r[(1-D1)(1-D2)(D3-Dr)(D3-D2)]^0.5/[Dr+D2-(D3+1) ] We also determine the optimal coding scheme which achieves the minimum total rate. We conclude the thesis by comparing the scenario of CVC-PL with two frames with a coding scheme, in which both of the sources are available at the encoders, i.e. distributed source coding versus centralized source coding. We show that for small D2 or large D3, the distributed source coding can perform as good as the centralized source coding. Finally, we talk about future work and extend and formulate the problem for M sources

Secure Multiterminal Source Coding with Side Information at the Eavesdropper

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate --average uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger-Tung and the secure source coding setups. Inner and outer bounds on the so called rates-distortion-equivocation region are derived. The inner region turns to be tight for two cases: (i) uncoded side information at Bob and (ii) lossless reconstruction of both sources at Bob --secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (resp.) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a non-zero distortion at Bob can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table

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/