arXiv subjects

Yair Be'ery

Publications and source records attributed to Yair Be'ery.

15 recordsLinked to original sources

arXiv2023

CRC-Aided Learned Ensembles of Belief-Propagation Polar Decoders

Polar codes have promising error-correction capabilities. Yet, decoding polar codes is often challenging, particularly with large blocks, with recently proposed decoders based on list-decoding or neural-decoding. The former applies multiple decoders or the same decoder multiple times with some redundancy, while the latter family utilizes emerging deep learning schemes to learn to decode from data. In this work we introduce a novel polar decoder that combines the list-decoding with neural-decoding, by forming an ensemble of multiple weighted belief-propagation (WBP) decoders, each trained to decode different data. We employ the cyclic-redundancy check (CRC) code as a proxy for combining the ensemble decoders and selecting the most-likely decoded word after inference, while facilitating real-time decoding. We evaluate our scheme over a wide range of polar codes lengths, empirically showing that gains of around 0.25dB in frame-error rate could be achieved. Moreover, we provide complexity and latency analysis, showing that the number of operations required approaches that of a single BP decoder at high signal-to-noise ratios.

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arXiv2022

Neural Decoding with Optimization of Node Activations

The problem of maximum likelihood decoding with a neural decoder for error-correcting code is considered. It is shown that the neural decoder can be improved with two novel loss terms on the node's activations. The first loss term imposes a sparse constraint on the node's activations. Whereas, the second loss term tried to mimic the node's activations from a teacher decoder which has better performance. The proposed method has the same run time complexity and model size as the neural Belief Propagation decoder, while improving the decoding performance by up to $1.1dB$ on BCH codes.

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arXiv2021

perm2vec: Graph Permutation Selection for Decoding of Error Correction Codes using Self-Attention

Error correction codes are an integral part of communication applications, boosting the reliability of transmission. The optimal decoding of transmitted codewords is the maximum likelihood rule, which is NP-hard due to the curse of dimensionality. For practical realizations, sub-optimal decoding algorithms are employed; yet limited theoretical insights prevent one from exploiting the full potential of these algorithms. One such insight is the choice of permutation in permutation decoding. We present a data-driven framework for permutation selection, combining domain knowledge with machine learning concepts such as node embedding and self-attention. Significant and consistent improvements in the bit error rate are introduced for all simulated codes, over the baseline decoders. To the best of the authors' knowledge, this work is the first to leverage the benefits of the neural Transformer networks in physical layer communication systems.

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arXiv2021

Deep Ensemble of Weighted Viterbi Decoders for Tail-Biting Convolutional Codes

Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine-learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, each decoder specializes in decoding words from a specific region of the channel words' distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high SNRs.

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arXiv2020

Data-Driven Ensembles for Deep and Hard-Decision Hybrid Decoding

Ensemble models are widely used to solve complex tasks by their decomposition into multiple simpler tasks, each one solved locally by a single member of the ensemble. Decoding of error-correction codes is a hard problem due to the curse of dimensionality, leading one to consider ensembles-of-decoders as a possible solution. Nonetheless, one must take complexity into account, especially in decoding. We suggest a low-complexity scheme where a single member participates in the decoding of each word. First, the distribution of feasible words is partitioned into non-overlapping regions. Thereafter, specialized experts are formed by independently training each member on a single region. A classical hard-decision decoder (HDD) is employed to map every word to a single expert in an injective manner. FER gains of up to 0.4dB at the waterfall region, and of 1.25dB at the error floor region are achieved for two BCH(63,36) and (63,45) codes with cycle-reduced parity-check matrices, compared to the previous best result of the paper "Active Deep Decoding of Linear Codes".

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arXiv2019

Active Deep Decoding of Linear Codes

High quality data is essential in deep learning to train a robust model. While in other fields data is sparse and costly to collect, in error decoding it is free to query and label thus allowing potential data exploitation. Utilizing this fact and inspired by active learning, two novel methods are introduced to improve Weighted Belief Propagation (WBP) decoding. These methods incorporate machine-learning concepts with error decoding measures. For BCH(63,36), (63,45) and (127,64) codes, with cycle-reduced parity-check matrices, improvement of up to 0.4dB at the waterfall region, and of up to 1.5dB at the errorfloor region in FER, over the original WBP, is demonstrated by smartly sampling the data, without increasing inference (decoding) complexity. The proposed methods constitutes an example guidelines for model enhancement by incorporation of domain knowledge from error-correcting field into a deep learning model. These guidelines can be adapted to any other deep learning based communication block.

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arXiv2018

Polar Decoding on Sparse Graphs with Deep Learning

In this paper, we present a sparse neural network decoder (SNND) of polar codes based on belief propagation (BP) and deep learning. At first, the conventional factor graph of polar BP decoding is converted to the bipartite Tanner graph similar to low-density parity-check (LDPC) codes. Then the Tanner graph is unfolded and translated into the graphical representation of deep neural network (DNN). The complex sum-product algorithm (SPA) is modified to min-sum (MS) approximation with low complexity. We dramatically reduce the number of weight by using single weight to parameterize the networks. Optimized by the training techniques of deep learning, proposed SNND achieves comparative decoding performance of SPA and obtains about $0.5$ dB gain over MS decoding on ($128,64$) and ($256,128$) codes. Moreover, $60 \%$ complexity reduction is achieved and the decoding latency is significantly lower than the conventional polar BP.

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arXiv2018

Joint Neural Network Equalizer and Decoder

Recently, deep learning methods have shown significant improvements in communication systems. In this paper, we study the equalization problem over the nonlinear channel using neural networks. The joint equalizer and decoder based on neural networks are proposed to realize blind equalization and decoding process without the knowledge of channel state information (CSI). Different from previous methods, we use two neural networks instead of one. First, convolutional neural network (CNN) is used to adaptively recover the transmitted signal from channel impairment and nonlinear distortions. Then the deep neural network decoder (NND) decodes the detected signal from CNN equalizer. Under various channel conditions, the experiment results demonstrate that the proposed CNN equalizer achieves better performance than other solutions based on machine learning methods. The proposed model reduces about $2/3$ of the parameters compared to state-of-the-art counterparts. Besides, our model can be easily applied to long sequence with $\mathcal{O}(n)$ complexity.

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arXiv2018

Improving Massive MIMO Belief Propagation Detector with Deep Neural Network

In this paper, deep neural network (DNN) is utilized to improve the belief propagation (BP) detection for massive multiple-input multiple-output (MIMO) systems. A neural network architecture suitable for detection task is firstly introduced by unfolding BP algorithms. DNN MIMO detectors are then proposed based on two modified BP detectors, damped BP and max-sum BP. The correction factors in these algorithms are optimized through deep learning techniques, aiming at improved detection performance. Numerical results are presented to demonstrate the performance of the DNN detectors in comparison with various BP modifications. The neural network is trained once and can be used for multiple online detections. The results show that, compared to other state-of-the-art detectors, the DNN detectors can achieve lower bit error rate (BER) with improved robustness against various antenna configurations and channel conditions at the same level of complexity.

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arXiv2018

Near Maximum Likelihood Decoding with Deep Learning

A novel and efficient neural decoder algorithm is proposed. The proposed decoder is based on the neural Belief Propagation algorithm and the Automorphism Group. By combining neural belief propagation with permutations from the Automorphism Group we achieve near maximum likelihood performance for High Density Parity Check codes. Moreover, the proposed decoder significantly improves the decoding complexity, compared to our earlier work on the topic. We also investigate the training process and show how it can be accelerated. Simulations of the hessian and the condition number show why the learning process is accelerated. We demonstrate the decoding algorithm for various linear block codes of length up to 63 bits.

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arXiv2017

RNN Decoding of Linear Block Codes

Designing a practical, low complexity, close to optimal, channel decoder for powerful algebraic codes with short to moderate block length is an open research problem. Recently it has been shown that a feed-forward neural network architecture can improve on standard belief propagation decoding, despite the large example space. In this paper we introduce a recurrent neural network architecture for decoding linear block codes. Our method shows comparable bit error rate results compared to the feed-forward neural network with significantly less parameters. We also demonstrate improved performance over belief propagation on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the RNN decoder can be used to improve the performance or alternatively reduce the computational complexity of the mRRD algorithm for low complexity, close to optimal, decoding of short BCH codes.

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arXiv2012

On Pseudocodewords and Improved Union Bound of Linear Programming Decoding of HDPC Codes

In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order of Bonferroni-type inequality in probability theory, and it is minimized by Prim's minimum spanning tree algorithm. The bound calculation needs the fundamental cone generators of a given parity-check matrix rather than only their weight spectrum, but involves relatively low computational complexity. It is targeted to high-density parity-check codes, where the number of their generators is extremely large and these generators are spread densely in the Euclidean space. We explore the generator density and make a comparison between different parity-check matrix representations. That density effects on the improvement of the proposed bound over the conventional LP union bound. The paper also presents a complete pseudo-weight distribution of the fundamental cone generators for the BCH[31,21,5] code.

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arXiv2011

On Pseudocodewords and Decision Regions of Linear Programming Decoding of HDPC Codes

In this paper we explore the decision regions of Linear Programming (LP) decoding. We compare the decision regions of an LP decoder, a Belief Propagation (BP) decoder and the optimal Maximum Likelihood (ML) decoder. We study the effect of minimal-weight pseudocodewords on LP decoding. We present global optimization as a method for finding the minimal pseudoweight of a given code as well as the number of minimal-weight generators. We present a complete pseudoweight distribution for the [24; 12; 8] extended Golay code, and provide justifications of why the pseudoweight distribution alone cannot be used for obtaining a tight upper bound on the error probability.

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arXiv2009

Efficient Linear Programming Decoding of HDPC Codes

We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts from redundant parity checks. Second, we propose an efficient mixed integer decoder utilizing the branch and bound method. We further enhance the proposed decoders by removing inactive constraints and by adapting the parity check matrix prior to decoding according to the channel observations. Based on simulation results the proposed decoders achieve near-ML performance with reasonable complexity.

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arXiv2009

Moderate-Density Parity-Check Codes

We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of ones of the parity-check matrix of the codes presented is typically higher than the number of ones of the parity-check matrix of low-density parity-check (LDPC) codes. But, still lower than those of the parity-check matrix of classical block codes. The proposed MDPC codes are cyclic and are designed by constructing idempotents using cyclotomic cosets. The construction is simple and allows finding short block-length, high-rate codes with good minimum distance. Inspired by some recent iterative soft-input soft-output (SISO) decoders used in a context of classical block codes, we propose a low complexity, efficient, iterative decoder called Auto-Diversity (AD) decoder. AD decoder is based on belief propagation (BP) decoder and takes advantage of the fundamental property of automorphism group of the constructed cyclic code.

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