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Lecture notes in networks and systems

Greedy Belief Propagation Algorithm for Low-Complexity LDPC Decoding

Yimo Zhen, Jinhui Chen, Zhan Zhang Xu, Ruxin Zhi

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.1007/978-981-96-5006-4_62

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Decoding for LDPC codes with enhanced residual belief-propagation

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This letter presents an enhanced list-based residual belief propagation (L-RBP) method for decoding low-density parity-check (LDPC) codes. L-RBP reduces computational complexity by scheduling a concise list of residuals. Moreover, the list is partially renewed to deter a small cluster of residuals from monopolizing renewal opportunities. Simultaneously, we also incorporate a decay mechanism to constrain the residuals retained within the list, further mitigating the greediness of the algorithm. The numerical results indicate that the L-RBP has an attractive convergence speed, error rate performance, and complexity of long-length and low-rate codes in the additive white Gaussian noise (AWGN) channel.
Four reliability-based high-efficient dynamic schedules (RHDS) for belief propagation (BP) decoding of low-density parity-check codes are proposed. The RHDS only processes one variable (or check) node, which has the maximum relative residual among all the variable (or check) nodes in each decoding iteration, thus keeping less greediness and decreasing complexity in comparison with egde-wise variable-to-check residual belief propagation (VC-RBP) algorithm. Simulation results show that RHDS's convergence rate is higher than VC-RBP while still keeping very low computational complexity.
To improve the performance of BP decoding for polar codes, researchers have developed a Belief Propagation List (BPL) decoding algorithm by executing multiple BP decoders in parallel.This algorithm outperforms traditional BP decoding based on single graph decoding, although it sacrifices some complexity and delay.Unlike this basic Polar-BPL decoding mentioned above, a low-density parity check like (LDPC-like) BPL decoding algorithm has been introduced into polar codes.This algorithm performs more efficient BP decoding iterations on sparse graphs.To further reduce the complexity and delay of LDPC-like BPL, and avoid analyzing all sparse graphs, this article proposes an improved LDPC-like BPL (ILDPC-like BPL) decoding algorithm based on selecting factor graphs.This algorithm analyzes differences in permuted factor graphs and selects these graphs with non-convergent decoding results to form a decoding list, allowing decoding to be completed with fewer graphs traversed and iterations, thereby reducing complexity and delay.On this basis, to improve the reliability of this algorithm, this article further adds a path metric (PM) mechanism, which can dynamically evaluate different sparse graphs' results in parallel decoding.The simulation results show that compared with LDPC-like BPL (random scheme), ILDPC-like BPL improves decoding performance while reducing decoding delay and complexity; Compared with basic Polar-BPL (cycle-shift scheme), this algorithm greatly reduces decoding delay and complexity while achieving similar performance.