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Hybrid Decoding of LDPC Codes

Ligter, Luca

Published Jan 1, 2023• 0 citations
OpenAlex

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Monte Carlo Markov chain (MCMC) decoding is a randomized algorithm which has been proven to be near-optimal in terms of decoding error probability. However, the exponentially slow mixing rate of Markov chains seems to preclude MCMC decoding from applications concerning even short blocklength codes. In contrast, belief propagation (BP) is a deterministic algorithm that is empirically fast but sub-optimal in error rate when it is used to decode low-density parity-check (LDPC) codes. In this paper, a code-independent BP-MCMC hybrid decoder is devised for short-blocklength LDPC codes. Theoretical error analysis of the hybrid algorithm is provided. Preliminary experiments show that the preprocessing of BP successfully reduces the time complexity of MCMC decoding and hence significantly improves the applicability of MCMC decoders to short LDPC codes.

Globecom•Dec 1, 2020•3 citations
In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.
Monte Carlo Markov chain (MCMC) decoding is a randomized algorithm which has been proven to be near-optimal in terms of decoding error probability. However, the exponentially slow mixing rate of Markov chains seems to preclude MCMC decoding from applications concerning even short blocklength codes. In contrast, belief propagation (BP) is a deterministic algorithm that is empirically fast but sub-optimal in error rate when it is used to decode low-density parity-check (LDPC) codes. In this paper, a code-independent BP-MCMC hybrid decoder is devised for short-blocklength LDPC codes. Theoretical error analysis of the hybrid algorithm is provided. Preliminary experiments show that the preprocessing of BP successfully reduces the time complexity of MCMC decoding and hence significantly improves the applicability of MCMC decoders to short LDPC codes.