Decimation Strategies for Belief Propagation Decoding of Quantum LDPC Codes

Due to code degeneracy and the graph structure of quantum low-density parity-check (QLDPC) codes, the performance of conventional belief propagation (BP) decoding can be poor. Recently, belief propagation guided decimation (BPGD) has shown promise to combat these challenges. In this paper, we investigate various decimation approaches to improve the error correcting performance and convergence speed of BPGD. We first consider soft decimation, where the BP equations are modified via several tuneable parameters. This approach exhibits linear complexity relative to the length of the block code and is shown to outperform hard decimation approaches for careful selection of the algorithm parameters. We then combine the approaches in a "soft-hard" BPGD variant, where hard decisions are periodically made and those symbols are permanently fixed throughout the remainder of the decoding process. Simulation results show that further performance improvement can be observed in this case at the cost of increasing the algorithmic complexity.