Detecting Minimum Distance of LDPC Codes with Improved Approximately Nearest Codeword Method

Approximately nearest codeword (ANC) is a classic approach for detecting minimum distance of low-density parity-check (LDPC) codes. With the principle of local search, ANC method is capable of detecting minimum distance of LDPC codes within acceptable time. However, the message passing (MP) decoding algorithm and scheduling scheme, as well as the local search strategy, still have much space to improve. To fill the gap, this paper proposes an improved-ANC method which employs novel noise introduction method, decoding algorithm, scheduling scheme and searching strategy, to accelerate the computation of the minimum distance of LDPC codes significantly. Finally, we run simulations on LDPC codes in Wi-Fi5 and 5G-NR standards. The simulation results are presented and demonstrate the effectiveness of our proposal.