Efficient Search and Elimination of Harmful Objects for the Optimization of QC-SC-LDPC Codes

The error correction performance of low-density parity-check codes under iterative message-passing decoding is degraded by the presence of certain harmful objects existing in their Tanner graph representation. Depending on the context, such harmful objects are known as stopping sets, trapping sets, absorbing sets, or pseudocodewords. In this paper, we propose a general procedure, based on edge spreading, that enables the design of good quasi-cyclic spatially coupled low-density parity-check codes. These codes are derived from quasi-cyclic low-density parity-check (QC-LDPC) block codes and possess a significantly reduced multiplicity of harmful objects with respect to the original QC-LDPC block codes. The proposed procedure relies on a novel algorithm that greedily spans the search space of potential candidates to reduce the multiplicity of the target harmful objects. The effectiveness of the method is validated via examples and numerical computer simulations.