Performance of Product Codes and Related Structures with Iterated Decoding

Several modifications of product codes have been suggested as standards for optical networks. We show that the performance exhibits a threshold that can be estimated from a result about random graphs. For moderate input bit error probabilities, the output error rates for codes of finite length can be found by easy simulations.

The analysis indicates that the performance curve can be extrapolated until the error floor is reached. The analysis allows us to calculate the error floors and avoid time-consuming simulations.