Neural Belief Propagation Decoding of CRC-Polar Concatenated Codes

Polar codes are the first class of error correcting codes that provably achieve the channel capacity at infinite code length. They were selected for use in the fifth generation of cellular mobile communications (5G). In practical scenarios such as 5G, a cyclic redundancy check (CRC) is concatenated with polar codes to improve their finite length performance. This is mostly beneficial for sequential successive-cancellation list decoders. However, for parallel iterative belief propagation (BP) decoders, CRC is only used as an early stopping criterion with incremental error-correction performance improvement. In this paper, we first propose a CRC-polar BP (CPBP) decoder by exchanging the extrinsic information between the factor graph of the polar code and that of the CRC. We then propose a neural CPBP (NCPBP) algorithm which improves the CPBP decoder by introducing trainable normalizing weights on the concatenated factor graph. Our results on a 5G polar code of length 128 show that at the frame error rate of 10^(-5) and with a maximum of 30 iterations, the error-correction performance of CPBP and NCPBP are approximately 0.25 dB and 0.5 dB better than that of the conventional CRC-aided BP decoder, respectively, while introducing almost no latency overhead

Mitigating Clipping Effects on Error Floors under Belief Propagation Decoding of Polar Codes

In this work, we show that polar belief propagation (BP) decoding exhibits an error floor behavior which is caused by clipping of the log-likelihood ratios (LLR). The error floor becomes more pronounced for clipping to smaller LLR-values. We introduce a single-value measure quantifying a "relative error floor", showing, by exhaustive simulations for different lengths, that the error floor is mainly caused by inadequate clipping values. We propose four modifications to the conventional BP decoding algorithm to mitigate this error floor behavior, demonstrating that the error floor is a decoder property, and not a code property. The results agree with the fact that polar codes are theoretically proven to not suffer from error floors. Finally, we show that another cause of error floors can be an improper selection of frozen bit positions.Comment: ISWCS201

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"

Convolutional Neural Network-aided Bit-flipping for Belief Propagation Decoding of Polar Codes

Known for their capacity-achieving abilities, polar codes have been selected as the control channel coding scheme for 5G communications. To satisfy the needs of high throughput and low latency, belief propagation (BP) is chosen as the decoding algorithm. However, in general, the error performance of BP is worse than that of enhanced successive cancellation (SC). Recently, critical-set bit-flipping (CS-BF) is applied to BP decoding to lower the error rate. However, its trial and error process result in even longer latency. In this work, we propose a convolutional neural network-assisted bit-flipping (CNN-BF) mechanism to further enhance BP decoding of polar codes. With carefully designed input data and model architecture, our proposed CNN-BF can achieve much higher prediction accuracy and better error correction capability than CS-BF but with only half latency. It also achieves a lower block error rate (BLER) than SC list (CA-SCL).Comment: 5 pages, 6 figure

Deep Learning-based Polar Code Design

In this work, we introduce a deep learning-based polar code construction algorithm. The core idea is to represent the information/frozen bit indices of a polar code as a binary vector which can be interpreted as trainable weights of a neural network (NN). For this, we demonstrate how this binary vector can be relaxed to a soft-valued vector, facilitating the learning process through gradient descent and enabling an efficient code construction. We further show how different polar code design constraints (e.g., code rate) can be taken into account by means of careful binary-to-soft and soft-to-binary conversions, along with rate-adjustment after each learning iteration. Besides its conceptual simplicity, this approach benefits from having the "decoder-in-the-loop", i.e., the nature of the decoder is inherently taken into consideration while learning (designing) the polar code. We show results for belief propagation (BP) decoding over both AWGN and Rayleigh fading channels with considerable performance gains over state-of-the-art construction schemes.Comment: Allerton201

Syndrome-Enabled Unsupervised Learning for Neural Network-Based Polar Decoder and Jointly Optimized Blind Equalizer

Recently, the syndrome loss has been proposed to achieve "unsupervised learning" for neural network-based BCH/LDPC decoders. However, the design approach cannot be applied to polar codes directly and has not been evaluated under varying channels. In this work, we propose two modified syndrome losses to facilitate unsupervised learning in the receiver. Then, we first apply it to a neural network-based belief propagation (BP) polar decoder. With the aid of CRC-enabled syndrome loss, the BP decoder can even outperform conventional supervised learning methods in terms of block error rate. Secondly, we propose a jointly optimized syndrome-enabled blind equalizer, which can avoid the transmission of training sequences and achieve global optimum with 1.3 dB gain over non-blind minimum mean square error (MMSE) equalizer.Comment: 12 pages, 13 figures, 3 tables. Published in IEEE Journal on Emerging and Selected Topics in Circuits and System

A Gated Hypernet Decoder for Polar Codes

Hypernetworks were recently shown to improve the performance of message passing algorithms for decoding error correcting codes. In this work, we demonstrate how hypernetworks can be applied to decode polar codes by employing a new formalization of the polar belief propagation decoding scheme. We demonstrate that our method improves the previous results of neural polar decoders and achieves, for large SNRs, the same bit-error-rate performances as the successive list cancellation method, which is known to be better than any belief propagation decoders and very close to the maximum likelihood decoder.Comment: Accepted to ICASSP 202

Deep Unfolding for Communications Systems: A Survey and Some New Directions

Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems. This survey summarizes the principle of deep unfolding and discusses its recent use for communication systems with focus on detection and precoding in multi-antenna (MIMO) wireless systems and belief propagation decoding of error-correcting codes. To showcase the efficacy and generality of deep unfolding, we describe a range of other tasks relevant to communication systems that can be solved using this emerging paradigm. We conclude the survey by outlining a list of open research problems and future research directions.Comment: IEEE Workshop on Signal Processing Systems (SiPS) 2019, special session on "Practical Machine-Learning-Aided Communications Systems.

Optimizing Polar Codes Compatible with Off-the-Shelf LDPC Decoders

Previous work showed that polar codes can be decoded using off-the-shelf LDPC decoders by imposing special constraints on the LDPC code structure, which, however, resulted in some performance degradation. In this paper we show that this loss can be mitigated; in particular, we demonstrate how the gap between LDPC-style decoding and Arikan's Belief Propagation (BP) decoding of polar codes can be closed by taking into account the underlying graph structure of the LDPC decoder while jointly designing the polar code and the parity-check matrix of the corresponding LDPC-like code. The resulting polar codes under conventional LDPC-style decoding are shown to have similar error-rate performance when compared to some well-known and standardized LDPC codes. Moreover, we obtain performance gains in the high SNR region.Comment: ITW201

AI for 5G: Research Directions and Paradigms

The 5th wireless communication (5G) techniques not only fulfil the requirement of $1,000$ times increase of internet traffic in the next decade, but also offer the underlying technologies to the entire industry and ecology for internet of everything. Compared to the existing mobile communication techniques, 5G techniques are more-widely applicable and the corresponding system design is more complicated. The resurgence of artificial intelligence (AI) techniques offers as an alternative option, which is possibly superior over traditional ideas and performance. Typical and potential research directions to which AI can make promising contributions need to be identified, evaluated, and investigated. To this end, this overview paper first combs through several promising research directions of AI for 5G, based on the understanding of the 5G key techniques. Also, the paper devotes itself in providing design paradigms including 5G network optimization, optimal resource allocation, 5G physical layer unified acceleration, end-to-end physical layer joint optimization, and so on.Comment: This paper is an overview paper composed in Englis