A low-complexity BP-OSD algorithm for quantum LDPC codes

This paper introduces a low-complexity belief propagation (BP) algorithm combined with ordered statistics decoding (OSD), referred to as the BP-OSD algorithm, for quantum low-density parity-check (LDPC) codes. In the pre-processing stage, we optimize the parameters of BP to reduce the average number of iterations. In the post-processing stage, we introduce a locally constrained OSD (LCOSD) scheme instead of the conventional OSD scheme. Additionally, we propose two early termination strategies to reduce the average number of searches in the post-processing stage. Numerical results demonstrate that: a) the proposed BP-OSD algorithm achieves performance comparable to (or slightly better than) that of the conventional BP-OSD algorithm; b) the parameter optimization in the pre-processing stage effectively reduces the average number of iterations; c) the proposed early termination strategies significantly reduce the average number of searches in the post-processing stage, often reducing the count to below ten and sometimes even to a single search.