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arXiv:2402.13948 · Globecom

Improved Syndrome-based Neural Decoder for Linear Block Codes

Gastón De Boni Rovella, Meryem Benammar

Published Dec 4, 2023• 4 citations
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Abstract

In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We improve on previous works in terms of allowing full decoding of the message rather than codewords, allowing thus the application to non-systematic codes, and proving that the single-message training property is still viable. The suggested system is implemented and tested on polar codes of sizes (64,32) and (128,64), and a BCH of size (63,51), leading to a significant improvement in both Bit Error Rate (BER) and Frame Error Rate (FER), with gains between 0.3dB and 1dB for the implemented codes in the high Signal-to-Noise Ratio (SNR) regime.

DOI
10.1109/globecom54140.2023.10436980

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In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We improve on previous works in terms of allowing full decoding of the message rather than codewords, allowing thus the application to non-systematic codes, and proving that the single-message training property is still viable. The suggested system is implemented and tested on polar codes of sizes (64,32) and (128,64), and a BCH of size (63,51), leading to a significant improvement in both Bit Error Rate (BER) and Frame Error Rate (FER), with gains between 0.3dB and 1dB for the implemented codes in the high Signal-to-Noise Ratio (SNR) regime.
In this work, we introduce a framework that enables the use of Syndrome-Based Neural Decoders (SBND) for high-order Bit-Interleaved Coded Modulations (BICM). To this end, we extend the previous results on SBND, for which the validity is limited to Binary Phase-Shift Keying (BPSK), by means of a theoretical channel modeling of the bit Log-Likelihood Ratio (bit-LLR) induced outputs. We implement the proposed SBND system for two polar codes (64, 32) and (128, 64), using a Recurrent Neural Network (RNN) and a Transformer-based architecture. Both implementations are compared in Bit Error Rate (BER) performance and computational complexity.
In this work, we introduce a framework that enables the use of Syndrome-Based Neural Decoders (SBND) for high-order Bit-Interleaved Coded Modulations (BICM). To this end, we extend the previous results on SBND, for which the validity is limited to Binary Phase-Shift Keying (BPSK), by means of a theoretical channel modeling of the bit Log-Likelihood Ratio (bit-LLR) induced outputs. We implement the proposed SBND system for two polar codes (64,32)(64,32)(64,32) and (128,64)(128,64)(128,64), using a Recurrent Neural Network (RNN) and a Transformer-based architecture. Both implementations are compared in Bit Error Rate (BER) performance and computational complexity.
Polar codes with large kernels offer improved error-correction performance but suffer from high decoding complexity due to costly marginalization operations. In this work, we propose neural network (NN)-based approximations of these marginalization functions, enabling efficient decoding for arbitrary linear kernels. We show that training on all-zero partial codewords is sufficient for linear kernels, significantly reducing the dataset size and allowing for smaller, faster NN models. Our method is evaluated within a Successive Cancellation (SC) decoder, being compatible with any blocklength, code rate, or SNR. Experimental results for kernel size 16 demonstrate strong performance and substantial complexity savings over exact marginalization.
The problem of decoding an (n, k, d) error-correcting block code, where a k-bit message word is mapped to an n-bit codeword, can be cast as a single-label classification problem. While it has been observed that the performance of such single-label neural decoders closely approaches that of the corresponding maximum likelihood decoder (MLD), the number of output nodes increases exponentially with k, making it prohibitive to implement for large k. To address this issue, we explore classification based multi-label neural decoders, in which the number of output nodes increases linearly with k. We consider well-known linear and non-linear block codes, as well as concatenated block codes, which have applications in emerging wireless networks. Our study finds that (i) although the number of output nodes linearly increases with k in a multi-label decoder, it requires more hidden layers and nodes in each hidden layer than the corresponding single-label decoder to achieve its best performance, and (ii) although one can design a multi-label decoder with bit error rate matching that of the MLD, it leaves more blocks in error leading to a reduced performance in terms of block error rate. We also note that the performance of the proposed decoder for concatenated codes is at least as good as that of a natural decoding algorithm in which the inner code is first decoded using the MLD and then the outer code is decoded with a polynomial-time decoding algorithm.
In this paper, we introduce the syndrome loss, an alternative loss function for neural error-correcting decoders based on a relaxation of the syndrome. The syndrome loss penalizes the decoder for producing outputs that do not correspond to valid codewords. We show that training with the syndrome loss yields decoders with consistently lower frame error rate for a number of short block codes, at little additional cost during training and no additional cost during inference. The proposed method does not depend on knowledge of the transmitted codeword, making it a promising tool for online adaptation to changing channel conditions.
In this paper, we introduce the syndrome loss, an alternative loss function for neural error-correcting decoders based on a relaxation of the syndrome. The syndrome loss penalizes the decoder for producing outputs that do not correspond to valid codewords. We show that training with the syndrome loss yields decoders with consistently lower frame error rate for a number of short block codes, at little additional cost during training and no additional cost during inference. The proposed method does not depend on knowledge of the transmitted codeword, making it a promising tool for online adaptation to changing channel conditions.