In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB.

Contents Table of Abbreviations x Glossary xi Summary xvi Declaration xvii Acknowledgement xviii 1 Introduction 1 1.1 Digital Communication and Error Control Coding : : : : : : : : : : : : : : : : : 1 1.2 Trellis Coding : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.3 Performance Estimation for Trellis Codes : : : : : : : : : : : : : : : : : : : : : : 4 1.4 Overview of the Thesis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2 System Models and Basics 7 2.1 Trellis Codes : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.1.1 Convolutional Codes : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.1.2 TCM Codes : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.1.3 CPM Schemes : : : : : : : : : : : : : : : : : : : : :

Code Design Based on Metric-Spectrum and Applications. (December 2004) Panayiotis D. Papadimitriou, B.S., University of Patras, Greece; M.S., University of Patras, Greece Chair of Advisory Committee: Dr. Costas N. Georghiades We introduced nested search methods to design (n, k) block codes for arbitrary channels by optimizing an appropriate metric spectrum in each iteration. For a given k, the methods start with a good high rate code, say k/(k + 1), and successively design lower rate codes up to rate k/2 corresponding to a Hadamard code. Using a full search for small binary codes we found that optimal or near-optimal codes of increasing length can be obtained in a nested manner by utilizing Hadamard matrix columns. The codes can be linear if the Hadamard matrix is linear and non-linear otherwise. The design methodology was extended to the generic complex codes by utilizing columns of newly derived or existing unitary codes. The inherent nested nature of the codes make them ideal for progressive transmission.