Symbol-Level Stochastic Chase Decoding of Reed-Solomon and BCH Codes

Abstract

This paper proposes the symbol-level-stochastic Chase decoding algorithm (S-SCA) for the Reed–Solomon (RS) and Bose–Chaudhuri–Hocquenghem (BCH) codes, which is a soft-input soft-output (SISO) decoder. By the efficient usage of void space between constellation points for $q$ -ary modulations and using soft information at the input of the decoder, the S-SCA is capable of outperforming conventional symbol-level-Chase algorithm (S-CA) with a less computational cost. Since the S-SCA starts with the randomized generation of likely test-vectors, it reduces the complexity to polynomial order and also it does not need to find the least reliable symbols to generate test-vectors. The symbol-level-search bitwise-transmission stochastic Chase algorithm (SSBT-SCA) is also introduced for RS codes over binary phase shift keying (BPSK) transmission that is capable of generating symbol-level test-vectors with reduced complexity and to better mitigate burst errors. Simulation results show that by increasing the number of test-vectors, the performance of the algorithm can asymptotically approach the maximum-likelihood (ML) bound. The S-SCA provides near 2 dB decoding gain in comparison with S-CA for a (31, 25) RS code using 32-QAM, when 1024 test-vectors are used. Furthermore, the algorithm provides near 3 dB additional gain with 1024 test-vectors compared with S-CA that uses 65536 iterations when a (255, 239) RS code is used in an additive white Gaussian noise (AWGN) channel. For the Rayleigh fading channel and the same code, the algorithm provides more than 5 dB gain. Furthermore, for (63, 57) BCH codes and 8-PSK modulation, the proposed algorithm provides 3 dB gain with less complexity.