Decoding via Sampling

We propose a novel decoding algorithm called “sampling decoding”, which is constructed using a Markov Chain Monte Carlo (MCMC) method and implements Maximum a Posteriori Probability decoding in an approximate manner. It is also shown that sampling decoding can be easily extended to universal coding or to be applicable for Markov sources. In simulation experiments comparing the proposed algorithm with the sum-product decoding algorithm, sampling decoding is shown to perform better as sample size increases, although decoding time becomes proportionally longer. The mixing time, which measures how large a sample size is needed for the MCMC process to converge to the limiting distribution, is evaluated for a simple coding matrix construction.