Asymptotic performance of single parity-check product codes

This article investigates the asymptotic performance of single parity-check (SPC) product codes (PCs) from a decoding point of view. Specifically, the probability of bit error is bounded before and after the decoding of each dimension, similar to the analysis of "iterated codes" by Elias (1954). It is shown that the asymptotic probability of bit error can be driven to zero as the number of dimensions, and hence the block length, increases at signal-to-noise ratios (SNRs) within 2 dB of capacity over the additive white Gaussian noise (AWGN) channel.