Contributions to the design of trellis code modulation schemes for m-psk signal sets

In this thesis we study issues concerning the design of optimal Trellis Coded Modulation (TCM) schemes for multipath fading channels. TCM is a method of combining the aspects of coding and modulation to achieve power efficient communication over bandwidth limited channels. Ungerboeck designed the first practical TCM based communication system. Since then TCM has been widely used for communicating over a wide variety of channels ranging from the simple additive white gaussian noise channels, partial response channels like those encountered in magnetic recording and data storage media, to frequency non-selective and selective channels encountered in mobile satellite communications, cellular telephony etc. to name a few. The design rules proposed by Ungerboeck result in TCM schemes with optimal distance properties. The design rules for TCM schemes that give the optimal performance, in terms of low bit error rates, over frequency non-selective channels has also been well studied.;In the first part of the thesis we analyze a complete communication system for a multipath fading channel with Rayleigh distributed fading. We analyze the performance of a receiver made up of a minimum mean squared-error decision feedback equalizer followed by a Viterbi decoder. Asymptotically tight upper bounds on the probability of a decoding error event are given. These bounds reveal the TCM parameters, or distance characteristics, that are critical to the performance over frequency selective channels.;In the second part of the thesis we study the problem of searching for encoder realizations that result in good TCM schemes for AWGN and fading channels. The problem of searching for the optimal encoder realizations is hard due to the lack of well defined relationship between the distance characteristics of the TCM scheme and the physical realization of the underlying encoder. A heuristic approach based on genentic algorithms has been studied and implemented. The encoder realizations found with this approach result in TCM schemes with better distance characteristics than the best known codes. Results on a comparison between a genetic algorithm based heuristic and random search approach are also presented.