This paper investigates the code search problem for trellis-coded multidimensional phase modulation for Rayleigh fading channels. New set partitionings for multiple phase-shift keying (M-PSK) are proposed using the effective code length (ECL) and the minimum product distance (PD) as the code design criteria. By using these set-partitionings rules, new multidimensional codes which are optimum for Rayleigh fading channels are constructed. The proposed codes compare favorably with the existing multidimensional trellis codes on fading channels in terms of bit error performance. The bit error performance is evaluated by simulation.

In this paper, a new methodology for design of MPSK trellis codes on fading channels is proposed. The proposed design criteria, based on effective code length, the minimum product distance and the minimum Euclidean distance are used to construct new 8-PSK and 16-PSK trellis codes with improved bit error rate performance on fading channels. The code performance is evaluated analytically and by Monte Carlo simulation. The results show that the proposed codes achieve significant improvements relative to the best known codes.>

New multilevel block codes for Rayleigh-fading channels are presented. At high signal-to-noise ratios (SNRs), the proposed block codes can achieve better bit error performance over TCM codes, optimum for fading channels, with comparable decoder complexity and bandwidth efficiency. The code construction is based on variant length binary component block codes. As component codes for the 8-PSK multilevel block construction, the authors propose two modified forms of Reed-Muller codes giving a good trade-off between the decoder complexity and the effective code rates. Code design criteria are derived from the error performance analysis. Multistage decoding shows very slight degradation of bit error performance relative to the maximum likelihood algorithm.>