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International Symposium on Turbo Codes and Iterative Information Processing

Error Structure Aware Parallel BP-RNN Decoders for Short LDPC Codes

Joachim Rosseel, Valérian Mannoni, Valentin Savin, Inbar Fijalkow

Published Aug 30, 2021• 3 citations
Publisher

Abstract

This article deals with the decoding of short block length Low Density Parity Check (LDPC) codes. It has already been demonstrated that Belief Propagation (BP) can be adjusted to the short coding length, thanks to its modeling by a Recurrent Neural Network (BP-RNN). To strengthen this adaptation, we introduce a new training method for the BP-RNN. Its aim is to specialize the BP-RNN on error events sharing the same structural properties. This approach is then associated with a new decoder composed of several parallel specialized BP-RNN decoders, each trained on correcting a different type of error events. Our results show that the proposed specialized BP-RNNs working in parallel effectively enhance the decoding capacity for short block length LDPC codes.

DOI
10.1109/istc49272.2021.9594200

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Spiking neural networks (SNNs) are neural networks that enable energy-efficient signal processing due to their event-based nature. This letter proposes a novel decoding algorithm for low-density parity-check (LDPC) codes that integrates SNNs into belief propagation (BP) decoding by approximating the check node update equations using SNNs. For the (273,191) and (1023,781) finite-geometry LDPC code, the proposed decoder outperforms sum-product decoder at high signal-to-noise ratios (SNRs). The decoder achieves a similar bit error rate to normalized sum-product decoding with successive relaxation. Furthermore, the novel decoding operates without requiring knowledge of the SNR, making it robust to SNR mismatch.
Iterative algorithms based on belief propagation can perform very close to optimal ML decoding for long LDPC codes. However, for short LDPC codes over Binary Erasure Channels (BEC) their performance drops significantly. In this paper, we introduce an iterative LDPC decoder over BEC by using our novel deep recurrent neural logic networks that learns Boolean logic algebra. It turned out that the neural logic network is capable of learning discrete algorithmic tasks and suitable for decoding LDPC codes. We show that the proposed decoding method can outperform the belief propagation algorithm for short LDPC code while using significantly fewer number of iterations. We further demonstrate that the proposed model is able to generalize very well. In other words, the model that was trained for specific settings such as channel erasure, parity check matrix, and code length, when tested under various other settings, still performed almost as if it was trained for those new settings.
BP decoding algorithm is one of the commonly used decoding algorithms for LDPC codes. To adapt LDPC codes to different 5G scenarios and further improve the decoding performance of short LDPC codes, a scheme combining model-driven deep learning with a traditional BP decoding algorithm is proposed. With the advantages of model-driven, this solution expands the decoding iteration process between the check node and the variable node into a neural network and proposes a parameter normalization optimization solution to solve the problem of the program with many training parameters, the edge weights of the optimized Tanner graph are re-assigned and bound. Simulation results show that the proposed scheme can improve the decoding performance of LDPC codes with short lengths.
In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.
Belief propagation (BP) decoding has been recognized for its capacity-approaching performance and high throughput when decoding long low-density parity-check (LDPC) codes. However, the application of BP decoding for short codes is hindered by dense parity-check matrices (PCMs) and prevalent short cycles in the Tanner graph. In this paper, we introduce a general method to extract an optimized sparse PCM for short binary block codes, which removes length-four cycles and enhances the connectivity of short cycles to enable BP decoding with improved performance. Notably, for short binary codes with lengths up to 64, our BP decoding performance approaches the maximum likelihood bound and surpasses the best-reported BP results with reduced computational complexity. Compared with other universal decoding algorithms, BP decoding using our extracted sparse PCMs is competitive in terms of both error-rate performance and computational complexity. These promising results suggest that our method to improve BP decoding for short codes is a step toward a practical universal BP decoder for next-generation communication systems.