Design and Performance of Trellis Codes for Wireless Channels

Abstract

Signal fading is one of the primary sources of performance degradation in mobile radio (wireless) systems. This dissertation addresses three different techniques to improve the performance of communication systems over fading channels, namely trellis coded modulation (TCM), space diversity and sequence maximum a posteriori decoding (MAP).<P>In the first part, TCM schemes that provide high coding gains over the flat, slow Rayleigh distributed fading channel are presented. It is shown that the use of two encoders in parallel used to specify the in-phase and quadrature components of the transmitted signal results in large performance improvements in bit error rates when compared with conventional TCM schemes in which a single encoder is used. Using this approach which we label ﲉ-Q TCM codes with bandwidth efficiencies of 1, 2, and 3 bits/sec/Hz are described for various constraint lengths. The performance of these codes is evaluated using tight upper bounds and simulation.<P>In the second part, the use of space diversity with three different combining schemes is investigated. Expressions for the cutoff rate parameter are shown for the three combining schemes over the fully interleaved Rayleigh-distributed flat fading channel. Also, tight upper bounds on the pairwise error probability are derived for the three combining schemes. Examples of I-Q TCM schemes with diversity combining are shown. The cutoff rate and a tight upper bound on the pairwise error probability are also derived for maximal ration combining with correlated branches.<P>In the last part the problem of reliably transmitting trellis coded signals over very noisy channels is considered. Sequence maximum a posteriori (MAP) decoding of correlated signals transmitted over very noisy AWGN and Rayleigh channels is presented. A variety of different systems with different sources, modulation schemes, encoder rates and complexities are simulated. Sequence MAP decoding proves to substantially improve the performance at very noisy channel conditions especially for systems with moderate redundancies and encoder rates. A practical example for coding the CELP line spectral parameters (LSPs) is also considered. Two source models are used. Coding gains of as much as 4 dB are achieved.