Parallel Monte Carlo Markov Chain Decoding of Linear Codes

A fast-converging Monte Carlo Markov chain decoding algorithm for linear codes over binary input memoryless channels is proposed. The new algorithm generates a small number of candidate estimates by simulating multiple Markov chains in parallel on the codebook, and performs a maximum likelihood decoding among the candidates. The key idea is to transform the generator matrix of the linear code into different systematic forms to construct distinct Markov chains for decoding. To demonstrate the practical feasibility of the proposed decoding algorithm, its performance is evaluated for Reed–Muller codes of length 64 and 128, including ℛℳ(2, 6), ℛℳ(3, 6), ℛℳ(2, 7), and ℛℳ(3, 7) over binary symmetric channels. Simulation results show that the proposed algorithm outperforms that of the recursive projection–aggregation algorithm by Ye and Abbe, and achieves a near-optimal performance.