An Achievable Rate-Distortion Region for the Multiple Descriptions Problem

A multiple-descriptions (MD) coding strategy is proposed and an inner bound to the achievable rate-distortion region is derived. The scheme utilizes linear codes. It is shown in two different MD set-ups that the linear coding scheme achieves a larger rate-distortion region than previously known random coding strategies. Furthermore, it is shown via an example that the best known random coding scheme for the set-up can be improved by including additional randomly generated codebooks

Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach

The classical theoretical framework for communication networks is based on the simplifying assumption that each message to be sent is known to a single transmitter and intended for a single receiver. Modern communication protocols reflect this framework by treating the physical layer as a network of individual links. However, this wireline view of wireless communications fails to account for the heterogeneous nature of network demands, consisting of both unicast and multicast services, and can fail to leverage the inherent broadcast advantage of the wireless medium. This thesis extends the classical framework of a private-message interface to the physical layer to one with both private and common messages. A key difficulty, in both the description and analysis of a communication model with general messages sets, is that there are combinatorially many message possibilities. With order-theoretic language and tools from combinatorial optimization and graphical models, we develop a general framework for characterizing the fundamental limits of information transfer over large many-to-one (multiple access) and one-to-many (broadcast) communication channels with general message sets. In particular, achievable regions are proposed for arbitrary such channels. For the multiple-access channel, the achievable region is optimal, and the order-theoretic perspective both unifies and extends previous results. For the broadcast channel, the region is specialized to an inner bound to the Degree of Freedom region, a setting where it is provably optimal in select cases. This thesis provides fresh insights into the long-standing random coding technique of superposition coding to arrive at these results. Governing constraints on reliable communication through superposition coding are shown to be polymatroidal over a lattice of subsets that may not be the boolean lattice of all subsets. Permissible input distributions for superposition coding are concisely characterized through directed graphical models of conditional dependencies. The two-user interference channel is also addressed, where the state-of-the art is extended from the case with two private messages to one with an additional common message

Structural Results for Coding Over Communication Networks

We study the structure of optimality achieving codes in network communications. The thesis consists of two parts: in the first part, we investigate the role of algebraic structure in the performance of communication strategies. In chapter two, we provide a linear coding scheme for the multiple-descriptions source coding problem which improves upon the performance of the best known unstructured coding scheme. In chapter three, we propose a new method for lattice-based codebook generation. The new method leads to a simplification in the analysis of the performance of lattice codes in continuous-alphabet communication. In chapter four, we show that although linear codes are necessary to achieve optimality in certain problems, loosening the closure restriction in the codebook leads to gains in other network communication settings. We introduce a new class of structured codes called quasi-linear codes (QLC). These codes cover the whole spectrum between unstructured codes and linear codes. We develop coding strategies in the interference channel and the multiple-descriptions problems using QLCs which outperform the previous schemes. In the second part, which includes the last two chapters, we consider a different structural restriction on codes used in network communication. Namely, we limit the `effective length' of these codes. First, we consider an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a new upper-bound on the correlation between the outputs of these functions. The upper-bound is presented as a function of the `dependency spectrum' of the corresponding Boolean functions. Next, we investigate binary block-codes (BBC). A BBC is defined as a vector of Boolean functions. We consider BBCs which are generated randomly, and using single-letter distributions. We characterize the vector of dependency spectrums of these BBCs. This gives an upper-bound on the correlation between the outputs of two distributed BBCs. Finally, the upper-bound is used to show that the large blocklength single-letter coding schemes in the literature are sub-optimal in various multiterminal communication settings.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137059/1/fshirani_1.pd