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arXiv:2508.20580

Precoded Polar Product Decoder Based on Soft-Output SCL Decoding and Maximization of Generalized Mutual Information

Nicolás Alvarez Prado, Andreas Straßhofer

Published Aug 28, 2025• 0 citations
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Abstract

We combine two approaches to optimize the iterative decoding of product codes with precoded polar component codes. On one side, we generate bitwise soft messages based on the codebook probability, an approximation of an auxiliary quantity that considers all valid decoding paths of a successive cancellation list (SCL) decoder. On the other side, we scale the soft information during message passing with offline-computed coefficients, which maximize the generalized mutual information (GMI) between the channel input and the outgoing message in each half iteration. Simulation results show significant improvement of the error-correcting performance compared to heuristic scaling and soft information generation based solely on the candidate list of the decoder. Moreover, we present an extrinsic version of the SCL decoder, which we use in a Monte Carlo density evolution analysis to derive decoding thresholds. The computed thresholds accurately predict the performance of the decoder.

DOI
10.48550/arxiv.2508.20580

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We combine two approaches to optimize the iterative decoding of product codes with precoded polar component codes. On one side, we generate bitwise soft messages based on the codebook probability, an approximation of an auxiliary quantity that considers all valid decoding paths of a successive cancellation list (SCL) decoder. On the other side, we scale the soft information during message passing with offline-computed coefficients, which maximize the generalized mutual information (GMI) between the channel input and the outgoing message in each half iteration. Simulation results show significant improvement of the error-correcting performance compared to heuristic scaling and soft information generation based solely on the candidate list of the decoder. Moreover, we present an extrinsic version of the SCL decoder, which we use in a Monte Carlo density evolution analysis to derive decoding thresholds. The computed thresholds accurately predict the performance of the decoder.
Iterative decoding of product codes with precoded polar component codes is optimized by combining two approaches. First, bitwise soft messages are generated by considering all valid decoding paths of a successive cancellation list (SCL) decoder. Second, the soft information during message passing is scaled with offline-computed coefficients that maximize the generalized mutual information of the channel input and the outgoing message in each half iteration. The method significantly improves the error-correcting performance compared to heuristic scaling and soft information generation based solely on the candidate list of the decoder. An extrinsic SCL decoder is used with a Monte Carlo density evolution analysis to derive iterative decoding thresholds that accurately predict the decoder performance.
Generalized low-density parity-check with polar component (GLDPC-PC) codes exhibit promising potential for 6G wireless systems with higher demands on reliability and data rate. The decoding method for GLDPC-PC codes involves belief propagation (BP), where the soft information of the component code is used as extrinsic information for check nodes. Although the Bahl-Cocke-Jelinek-Raviv (BCJR) decoding algorithm provides bitwise optimal soft information for linear block codes, its decoding complexity increases exponentially with the code length, making it impractical for applications. Therefore, the near-optimal soft-output successive cancellation list (SO-SCL) decoding with fixed scaling is proposed to reduce decoding complexity. However, the complexity of SO-SCL decoding still holds potential for further optimization. In this work, we propose an offline approximation of the unvisited probability codebook and a staged scaling strategy for the extrinsic information to reduce decoding complexity while maintaining low performance loss.
Although the successive cancellation list (SCL) decoding of polar codes exhibits excellent performance, it retains many decoding paths in the list with negligible contribution to the final output, resulting in high sorting and computational complexity. In this letter, we propose a novel pruning strategy to mitigate the decoding complexity. By leveraging the blockwise soft output extraction process of soft-output SCL and soft-output fast SCL decoding, we provide an accurate approximation of the probability that a decoding path is correct, and thus accordingly prune the paths failing to meet a pre-defined reliability threshold. The complexity reduction achieved by the proposed soft-output-based pruned SCL (SOP-SCL) decoder and its fast version, SOP-FSCL decoder, is significant, without any compromise in error-correction performance. Meanwhile, they also prove to be more efficient than state-of-the-art pruned polar decoders.
We present a novel successive cancellation list (SCL) decoding method for the polar codes based on the mutual-information values of the bit-channels. At short-to-medium blocklengths, only a certain fraction of the bit-channels get polarized. Usually the mutual-information values for the bit- channels are computed for the construction of the code. Using these available mutual-information values, we identify the information bits exhibiting full polarization and having high channel reliability. In the proposed mutual- information-based SCL (MI-SCL) decoder, only one emanating path is considered for such bits. This results in the reduction of the width of the decoding tree. Simulation results confirm the impressive performance of the MI-SCL decoder specially with concatenated cyclic redundancy check codes.
Although the successive cancellation list (SCL) decoding of polar codes exhibits excellent performance, it retains many decoding paths in the list with negligible contribution to the final output, resulting in high sorting and computational complexity. In this letter, we propose a novel pruning strategy to mitigate the decoding complexity. By leveraging the blockwise soft output extraction process of soft-output SCL and soft-output fast SCL decoding, we provide an accurate approximation of the probability that a decoding path is correct, and thus accordingly prune the paths failing to meet a pre-defined reliability threshold. The complexity reduction achieved by the proposed soft-output-based pruned SCL (SOP-SCL) decoder and its fast version, SOP-FSCL decoder, is significant, without any compromise in error-correction performance. Meanwhile, they also prove to be more efficient than state-of-the-art pruned polar decoders.
The soft-output successive cancellation list (SO-SCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder for polar codes. However, the sequential nature of SCL decoding leads to a high decoding latency for the SO-SCL decoder. In this paper, we propose a soft-output fast SCL (SO-FSCL) decoder by incorporating node-based fast decoding into the SO-SCL framework. Simulation results demonstrate that the proposed SO-FSCL decoder significantly reduces the decoding latency without loss of performance compared with the SO-SCL decoder.