On the bit-error rate of product accumulate codes in optical fiber communications

Product accumulate (PA) codes were proposed as a class of high-rate low-complexity, capacity-approaching codes on additive white Gaussian noise (AWGN) channels. In this paper, we investigate the performance of the PA codes on intensity modulated optical fiber channels where the amplified spontaneous emission (ASE) noise dominates all other noise sources. We consider binary on-off keying (OOK) modulation and iterative soft-decision message-passing decoding for the PA codes. Three channel models for the ASE noise dominated channel are investigated: asymmetric chi-square, asymmetric Gaussian, and symmetric Gaussian channels (i.e., AWGN). At low signal-to-noise ratios (SNRs), due to the lack of tight bounds, code performance is evaluated using simulations of typical PA coding schemes. For high SNRs that are beyond simulation capabilities, we derive the pairwise error probability of the three channels and explore an average upper bound on the bit-error rate over the ensemble of PA codes. We show that AWGN channels, although fundamentally different from chi-square channels, can serve as a reference to approximate the performance of high-rate PA codes.