Soft decoding of BCH codes applied to multilevel modulation codes for Rayleigh fading channels

8PSK multilevel codes (MLC) designed for fading channels with multistage decoding (MSD) are reported in this paper. Binary block BCH codes of medium length have been chosen to construct powerful MLC 8PSK schemes and an efficient soft decision decoding algorithm has been used in the MSD decoder. Error rate performances have been evaluated by simulations and compared favourably to the cutoff rate limit over Rayleigh channels. The new MSD decoding scheme presents several advantages compared to the usual method based on the Viterbi algorithm. The most interesting one is that the decoding complexity is not dependent of the trellis structure of the block codes, it can thus cope with the codes of medium length that are used to construct very powerful MLC 8PSK codes. Very few computations are necessary when the channel is under good conditions. When the channel is worse, the computation effort can be pre-limited, without important loss of performance. It has however a more complex structure and a variable processing delay. Simulations have been performed to evaluate the performance of the constructed MLC schemes, For the interesting bandwidth efficiencies ranged from 1.5 to 2.6 bits/s/Hz, very good error rate performances have been obtained. Comparison with the known codes and the cutoff rate limit revealed that these new MLC 8PSK codes are very powerful for information transmission over Rayleigh fading channels. The adopted soft decision decoding algorithm can be adapted to different levels of performance/complexity degree, so good performance/complexity trade-offs can be achieved for these MLC/MSD schemes for practical applications.