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

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

Capacity, Error Exponent, and Structural Results for Communication Networks

In various multi-terminal communication scenarios, contrary to point-to-point communication, characterization of fundamental limits such as capacity and error exponent is still an open problem. We study such fundamental limits and the structure of optimality achieving codes. This thesis consists of two parts: in the first part, we investigate the role of algebraic structures in multi-terminal communications. We show the necessity of various types of algebraic structure in capacity achieving codes and argue that the lack of such structures in the conventional random codes leads to their sub-optimality. We develop a new class of partially structured codes called quasi-structured code (QSC). Such codes span the spectrum from completely structured to completely unstructured codes. It is shown that the application of QSCs leads to improvements over the current coding strategies for many problems including distributed source coding and multiple-access channel (MAC) with feedback. In the second part of the thesis, we study the optimal error exponent in various multi-terminal communication scenarios. We derive a lower and upper bound on the error exponent of discrete memoryless MAC with noiseless feedback and variable-length codes (VLCs). The bounds increase linearly with respect to a specific Euclidean distance measure defined between the transmission rate pair and the capacity boundary. The bounds are shown to be tight for specific classes of MACs.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149959/1/mohsenhd_1.pd

RESOURCE ALLOCATION FOR WIRELESS RELAY NETWORKS

In this thesis, we propose several resource allocation strategies for relay networks in the context of joint power and bandwidth allocation and relay selection, and joint power allocation and subchannel assignment for orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiple access (OFDMA) systems. Sharing the two best ordered relays with equal power between the two users over Rayleigh flat fading channels is proposed to establish full diversity order for both users. Closed form expressions for the outage probability, and bit error probability (BEP) performance measures for both amplify and forward (AF) and decode and forward (DF) cooperative communication schemes are developed for different scenarios. To utilize the full potentials of relay-assisted transmission in multi user systems, we propose a mixed strategy of AF relaying and direct transmission, where the user transmits part of the data using the relay, and the other part is transmitted using the direct link. The resource allocation problem is formulated to maximize the sum rate. A recursive algorithm alternating between power allocation and bandwidth allocation steps is proposed to solve the formulated resource allocation problem. Due to the conflict between limited wireless resources and the fast growing wireless demands, Stackelberg game is proposed to allocate the relay resources (power and bandwidth) between competing users, aiming to maximize the relay benefits from selling its resources. We prove the uniqueness of Stackelberg Nash Equilibrium (SNE) for the proposed game. We develop a distributed algorithm to reach SNE, and investigate the conditions for the stability of the proposed algorithm. We propose low complexity algorithms for AF-OFDMA and DF-OFDMA systems to assign the subcarriers to the users based on high SNR approximation aiming to maximize the weighted sum rate. Auction framework is proposed to devise competition based solutions for the resource allocation of AF-OFDMA aiming tomaximize either vi the sum rate or the fairness index. Two auction algorithms are proposed; sequential and one-shot auctions. In sequential auction, the users evaluate the subcarrier based on the rate marginal contribution. In the one-shot auction, the users evaluate the subcarriers based on an estimate of the Shapley value and bids on all subcarriers at once

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th