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International Symposium on Turbo Codes and Iterative Information Processing

Decoding LDPC Codes on Binary Erasure Channels using Deep Recurrent Neural-Logic Layers

Ali Payani, Faramarz Fekri

Published Dec 1, 2018• 8 citations
Publisher

Abstract

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.

DOI
10.1109/istc.2018.8625326

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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.
This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.
For the Belief Propagation (BP) algorithm of low-density parity-check (LDPC) codes, existing deep learning methods have a limited performance improvement and it is difficult to train deep-level networks. In this paper, a model-driven quasi-residual network (Quasi-ResNet) BP decoding architecture is proposed for LDPC codes to further improve the performance of standard BP decoding. This method feeds the reliable messages calculated in current iteration into the next iteration based on the shortcut connection, and adjusts the weight of shortcut connection based on the error Back Propagation algorithm of neural network to determine the optimal genetic proportion of reliable messages. The decoding architecture is composed of a model-driven deep neural network (DNN) and shortcut connection. Simulation results show that the decoder can not only unfold more layers quickly compared with the DNN-based BP decoder, but also further improve the decoding performance.
In this paper, we propose a new approach to design finite alphabet iterative decoders (FAIDs) for Low-Density Parity Check (LDPC) codes over binary symmetric channel (BSC) via recurrent quantized neural networks (RQNN). We focus on the linear FAID class and use RQNNs to optimize the message update look-up tables by jointly training their message levels and RQNN parameters. Existing neural networks for channel coding work well over Additive White Gaussian Noise Channel (AWGNC) but are inefficient over BSC due to the finite channel values of BSC fed into neural networks. We propose the bit error rate (BER) as the loss function to train the RQNNs over BSC. The low precision activations in the RQNN and quantization in the BER cause a critical issue that their gradients vanish almost everywhere, making it difficult to use classical backward propagation. We leverage straight-through estimators as surrogate gradients to tackle this issue and provide a joint training scheme. We show that the framework is flexible for various code lengths and column weights. Specifically, in high column weight case, it automatically designs low precision linear FAIDs with superior performance, lower complexity, and faster convergence than the floating-point belief propagation algorithms in waterfall region.
Low-density parity-check (LDPC) codes have been one of the most popular error correction candidates in modern communication and data storage systems for the past three decades due to their capacity-approaching error correction capability under the Belief Propagation (BP) decoding algorithms. In this dissertation, we investigate three topics related to efficient and effective decoding algorithms and the code design of LDPC codes. In the first part of this dissertation, we propose a methodology with the help of artificial intelligence to design Finite Alphabet Iterative Decoders (FAID) for LDPC codes, which are not only of great theoretical but also practical importance. This model-driven neural network (NN) framework unfolds the decoding iterations, introduces quantized neural networks (QNN) to model the FAIDs, and proposes a new cost function, namely, bit error rate (BER), to address the inefficiency in discrete-output channel scenarios. The low precision activations in the QNN and quantization in the cost functions cause a critical issue that their gradients vanish almost everywhere, making it difficult to use classical backward propagation. We design and leverage straight-through estimators as surrogate gradients to tackle this issue and provide a joint training scheme. These QNN-aided FAIDs, are capable of surpassing the floating-point BP algorithms, with much lower complexity and faster convergence. The QNN-aided approach is general, as it can be applied to both continuous and discrete-output channels. In the second part of this dissertation, we propose a new code construction of LDPC codes based on the conventional parity-check matrices of Reed-Solomon (RS) codes. We investigate the girth and cycle structure and introduce an efficient searching algorithm to reduce short cycles in their Tanner graphs and to construct LDPC codes with a girth of at least eight. We use masking to further reduce the number of short cycles and to adjust the column and row weights of the parity-check matrices of the constructed codes for performance improvement. Our designs are systematic and flexible, which balance the requirements of good waterfall performance and low error-floor while maintaining a structure that facilitates implementation. In the third part of this dissertation, we investigate binary quasi-cyclic (QC) LDPC codes and their capability to correct phased bursts of erasures. We prove that the peeling algorithm when applied to such parity-check matrices of column weight two can correct all erasures that can be corrected by a maximum likelihood (ML) decoder. We show that by modifying the parity-check matrices of column weight two and globally coupling them, the erasure correcting capability can be further enhanced. For the Additive White Gaussian Noise (AWGN) channel, we design QC LDPC codes with parity-check matrices of column weight three or more that can correct phased bursts of erasures and perform well over the AWGN channel. Our analysis of QC-LDPC codes with parity-check matrices of column weight two is rather comprehensive as we determine, for all such codes, their dimensions, minimum Hamming distances, and their capabilities to correct phased bursts.
LDPC codes, as an error correcting code close to the Shannon limit, are widely used in modern communication systems such as 5 G, satellite communication, deep space communication, and other fields. Traditional LDPC decoding algorithms, such as belief propagation (BP) algorithm and its variants, have achieved good performance, but face challenges such as high complexity and slow convergence, especially when dealing with long code lengths and high noise scenarios. The rise of deep learning has brought new opportunities for LDPC decoding, and its powerful features learning and pattern recognition capabilities are expected to break through the bottleneck of traditional decoding. Based on the overview of deep neural network decoding methods for LDPC codes by data-driven and model driven approaches, this paper analysis and comparison of error rate performance of short codeH(8,16)\mathbf{H} (8,16)H(8,16)matrix by convolutional neural networks (CNN), residual network (ResNet), and Kolmogorov-Arnold Network (KAN).