Low-Complexity Soft-Decision Concatenated LDGM-Staircase FEC for High-Bit-Rate Fiber-Optic Communication

Abstract

A concatenated soft-decision forward error correction (FEC) scheme consisting of an inner low-density generator-matrix (LDGM) code and an outer staircase code is proposed. The soft-decision LDGM code is used for error reduction, while the majority of bit errors are corrected by the low-complexity hard-decision staircase code. Decoding complexity of the concatenated code is quantified by a score based on the number of edges in the LDGM code Tanner graph, the number of decoding iterations, and the number of staircase code decoding operations. The inner LDGM ensemble is designed by solving an optimization problem, which minimizes the product of the average node degree and an estimate of the required number of decoding iterations. A search procedure is used to find the inner and outer code pair with lowest complexity. The design procedure results in a Pareto-frontier characterization of the tradeoff between net coding gain and complexity for the concatenated code. Simulations of code designs at $\text{20}\%$ overhead showed that the proposed scheme achieves net coding gains equivalent to existing soft-decision FEC solutions, with up to $\text{57}\%$ reduction in complexity.