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-levelChase algorithm (S-CA) with a less computational cost. Since the S-SCA starts with the randomized generation of likely testvectors, it reduces the complexity to polynomial order and also it does not need to find the least reliable symbols to generate testvectors. 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.

A message passing (MP) algorithm for resource allocation (RA) in an Orthogonal Frequency Division Multiple Access (OFDMA) based spectrum sharing system is developed in this paper. We derive optimal power and subcarrier allocations. We further shed light on advantages of the MP algorithm particularly against the dual solution and highlight its suitability in reducing the computational burdens for practical configurations. It is observed that MP algorithm converges only after two iterations compared to 400 required iterations in the dual case. This considerably reduces the corresponding computational time, which in turn results in much lower consumed processing energy. The saved processing energy and time can then be exploited for enhancing the scheduled data rate especially when the number of users is high.