Low complexity product codes with LDPC codes achieving ultra low BER

Ultra low bit error rate (BER) is required in high speed communications such as the 100 Gbit/s long haul optic communications. In this paper, a type of simple product codes is proposed using low density parity check (LDPC) codes with very high rate algebraic block codes by exploiting the sparsity of LDPC decoding failure and sparse error distribution in an LDPC frame with errors. Specifically, different with traditional product codes, the information bits are first encoded with very high rate algebraic block codes of low encoding and decoding complexity. Even the block codes correcting a single error using algebraic decoding method can be used. Then, LDPC codes are used as the inner code to obtain a low decoding threshold using iterative decoding. This design scheme can achieve the ultra low bit error rate at relatively low signal-to-noise ratios. The cost of the proposed scheme is the relatively large latency, which is not so critical for the ultra high speed communications.