Design of non-binary decoders using the role model framework

The concept of a message-passing decoder for non-binary low-density parity-check (LDPC) codes that operates on symbol rankings instead of probability distributions is investigated. The optimal Bayesian conversion from ranks back to probabilities is derived, and the hypothetical performance of a rank-based algorithm is measured by converting the rank-valued messages back to probabilities and implementing the node operations in the probability domain. While the performance of a pure rank-based decoder is disappointing, further analysis and performance evaluation shows that a hybrid decoder that switches to the probability domain for its final iteratons exhibits a performance at par with the best known low complexity decoders without causing a significant increase in the overall number of iterations.