Optimization of SC-LDPC Codes for Window Decoding With Target Window Sizes

In this paper, we propose an optimization method for protograph-based spatially coupled low-density parity-check (SC-LDPC) codes under window decoding (WD). Previous works on constructing SC-LDPC codes for WD typically focused on optimizing asymptotic performance metrics such as the WD threshold. However, in this paper, it is observed that the WD threshold is not an appropriate metric to sufficiently explain the finite-length behavior of SC-LDPC codes under WD. Thus, we propose a new performance metric, called the window mean parameter, based on a scaling analysis to capture the WD performance more accurately and formulate a code optimization algorithm that optimizes the proposed performance metric. Since the proposed metric depends on the window size, the optimization algorithm can provide a code family of SC-LDPC codes optimized for various target window sizes. Simulation results confirm that the improvement in the proposed metric leads to a finite-length performance improvement, resulting in one to two orders of the frame error rate gain over the conventional SC-LDPC codes for a wide range of window sizes. Furthermore, we investigate structural characteristics of the proposed codes to provide a supplementary explanation for the performance improvement, which also promotes a better understanding of SC-LDPC codes for WD.