Bit error rate analysis on iterative two-stage decoding of two dimensional codes by importance sampling

We present a bit error rate analysis for iterative two-stage hard decision decoding of product codes and proposed a concatenated codes suitable for optical communication. Our method is based on an importance sampling technique characterized by recursive calculation of cumulative binomial probabilities and direct biasing of error patterns. We can accelerate the Monte Carlo simulations by several orders of magnitude such as 10⁸ and estimate the coding gains at the BERs as low as 10^-15 required in optical communications. We apply the method for comparative BER analysis of product codes and proposed concatenated codes and show that product codes of small minimum distance have error floors at low BERs while the proposed concatenated codes of large minimum distance do not.