Combined coding and modulation: theory and applications

Abstract

The theoretical aspects of the encoding process are investigated, resulting in a precise definition of linear codes together with theorems that clarify how they can be obtained. A particular subset of linear codes, called superlinear codes, for which the performance analysis is highly simplified is identified. The most relevant performance measures for the analysis of this class of codes are discussed. The minimum Euclidean distance and the event and bit error probabilities are found analytically using the uniform error property (when applicable) or variations on it. This yields accurate upper and lower bounds to the error rate at the price of reasonable computational complexity. The theory is then applied to the search for 'good' codes and to their performance evaluation. The cases of 16- and 32-PSK codes, which are good candidates for use in digital satellite transmission, are considered. Several new results in terms of error event and bit error probabilities are presented, showing considerable gains in terms of SNR with respect to the uncoded case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>