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IEEE Transactions on Cognitive Communications and Networking

Deep Learning-Assisted Adaptive Dynamic-SCLF Decoding of Polar Codes

Jun Li, Liangyu Zhou, Zhengquan Li, Weidong Gao, Ru Ji, Jintao Zhu, Ziyi Liu

Published Jan 3, 2024• 9 citations
Publisher

Abstract

Recently, the dynamic-successive cancellation list flip (D-SCLF) decoder has been proposed to improve the high-order flipping performance of existing successive cancellation list flip (SCLF) decoders in polar codes decoding. However, the D-SCLF decoder involves a large number of exponential and logarithmic operations, resulting in an exponential increase in computational complexity. To further improve the performance and reduce the average complexity of D-SCLF decoding, the deep learning-assisted adaptive dynamic-SCLF (DL-AD-SCLF) decoding is proposed in this paper. The error metric of D-SCLF decoding is re-derived, and an approximation scheme is proposed to reduce computational complexity. To compensate the loss of performance due to approximation, two learnable parameters are introduced. Customized neural network structures are proposed to optimize these learnable parameters according to the improved error metric by employing deep learning (DL), and the deep learning-assisted dynamic-SCLF (DL-D-SCLF) decoding is proposed. Furthermore, the adaptive list is introduced into the DL-D-SCLF decoding to further reduce decoding complexity. Simulation results show that the proposed decoder performance is improved up to 0.35dB and 0.25dB, the average complexity is reduced by up to 57.65% and 51.48% for single-bit and multi-bit flipping, respectively. Additionally, the proposed decoder exhibits good robustness to changes in code rates, code lengths, and channel conditions.

DOI
10.1109/tccn.2024.3349450

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Recently, the dynamic-successive cancellation list flip (D-SCLF) decoder has been proposed to improve the high-order flipping performance of existing successive cancellation list flip (SCLF) decoders in polar codes decoding. However, the D-SCLF decoder involves a large number of exponential and logarithmic operations, resulting in an exponential increase in computational complexity. To further improve the performance and reduce the average complexity of D-SCLF decoding, the deep learning-assisted adaptive dynamic-SCLF (DL-AD-SCLF) decoding is proposed in this paper. The error metric of D-SCLF decoding is re-derived, and an approximation scheme is proposed to reduce computational complexity. To compensate the loss of performance due to approximation, two learnable parameters are introduced. Customized neural network structures are proposed to optimize these learnable parameters according to the improved error metric by employing deep learning (DL), and the deep learning-assisted dynamic-SCLF (DL-D-SCLF) decoding is proposed. Furthermore, the adaptive list is introduced into the DL-D-SCLF decoding to further reduce decoding complexity. Simulation results show that the proposed decoder performance is improved up to 0.35dB and 0.25dB, the average complexity is reduced by up to 57.65% and 51.48% for single-bit and multi-bit flipping, respectively. Additionally, the proposed decoder exhibits good robustness to changes in code rates, code lengths, and channel conditions.
Designing an efficient decoder is an effective way to improve the performance of polar codes with limited code length. List flip decoders have received attention due to their good performance trade-off between list decoders and flip decoders. In particular, the newly proposed dynamic successive cancellation list flip (D-SCLF) decoder employs a new flip metric to effectively correct high-order errors and thus enhances the performance potential of present list flip decoders. However, this flip metric introduces extra exponential and logarithmic operations, and the number of these operations rises exponentially with the increase in the order of error correction and the number of information bits, which then limits its application value. Therefore, we designed an adaptive list flip (ALF) decoder with a new heuristic simplified flip metric, which replaces these extra nonlinear operations in the original flip metric with linear operations. Simulation results show that the simplified flip metric does not reduce the performance of the D-SCLF decoder. Moreover, based on the in-depth theoretical analyses of the combination of the adaptive list and the list flip decoders, the ALF decoder adopts the adaptive list to further reduce the average complexity.
Polar codes are the first error-correcting code proven to achieve channel capacity based on infinite code length. The Successive Cancellation List Flip (SCLF) decoding algorithm was proposed by flipping an erroneous bit during the next decoding attempt. To identify the erroneous bits, the Log-Likelihood Ratio (LLR) is used to indicate the reliability of each decision bit. To improve the accuracy of the erroneous bit prediction, we propose deep-learning-aided (DL-aided) SCLF decoding algorithms. We first offer a stacked LSTM network that contains new features to train our models, which are able to improve the accuracy of the prediction of positions of erroneous bits. Then we separately train the stacked LSTM models to predict the position of both the first and second erroneous bits and whether to continue flipping. As a result, the DL-aided SCLF decoding algorithms based on the proposed stacked LSTM flip-1 model, stacked LSTM flip-2 model, and the stacked LSTM continue-flipping check (CFC) model are able to provide a better performance at a lower number of average decoding attempts when compared to other state-of-the-art decoding algorithms.
Polar codes have attracted much attention in the past decade due to their capacity-achieving performance. The higher decoding capacity is required for 5G and beyond 5G (B5G). Although the cyclic redundancy check (CRC)- assisted successive cancellation list bit-flipping (CA-SCLF) decoders have been developed to obtain a better performance, the solution to error bit correction (bit-flipping) problem is still imperfect and hard to design. In this work, we leverage the expert knowledge in communication systems and adopt deep learning (DL) technique to obtain the better solution. A low-complexity long short-term memory network (LSTM)-assisted CA-SCLF decoder is proposed to further improve the performance of conventional CA-SCLF and avoid complexity and memory overhead. Our test results show that we can effectively improve the BLER performance by 0.11dB compared to prior work and reduce the complexity and memory overhead by over 30% of the network.
Successive cancellation list decoders with flip operations (SCL-Flip) can utilize re-decoding attempts to significantly improve the error-correction performance of polar codes. However, these re-decoding attempts result in extra computation complexity, which thus leads to increased energy consumption and decoding latency to the communication system adopting SCL-Flip decoders. To significantly reduce the computation complexity of current SCL-Flip decoders, we design a new adaptive SCL-Flip (AD-SCLF) decoder, which can be easily implemented based on existing SCL-Flip techniques. Simulation results showed that the AD-SCLF can reduce up to 80.85\% of the computational complexity of a current SCL-Flip decoder at a matched FER=10−3FER=10^{-3}FER=10−3. The result implies our decoder can significantly reduce the energy consumption caused by redundant re-decoding attempts from the SCL-Flip decoder.
This work presents a fast successive-cancellation list flip (Fast-SCLF) decoding algorithm for polar codes that addresses the high latency issue associated with the successive-cancellation list flip (SCLF) decoding algorithm. We first propose a bit-flipping strategy tailored to the state-of-the-art fast successive-cancellation list (FSCL) decoding that avoids tree-traversal in the binary tree representation of SCLF, thus reducing the latency of the decoding process. We then derive a parameterized path selection error model to accurately estimate the bit index at which the correct decoding path is eliminated from the initial FSCL decoding. The trainable parameter is optimized online based on an efficient supervised learning framework. Simulation results show that for a polar code of length 512 with 256 information bits, with similar error-correction performance and memory consumption, the proposed Fast-SCLF decoder reduces up to 73.4% of the average decoding latency of the SCLF decoder with the same list size at the frame error rate of 10−4, while incurring a maximum computational complexity overhead of 27.6%. For the same polar code of length 512 with 256 information bits and at practical signal-to-noise ratios, the proposed decoder with list size 4 reduces 89.3% and 43.7% of the average complexity and decoding latency of the FSCL decoder with list size 32 (FSCL-32), respectively, while also reducing 83.2% of the memory consumption of FSCL-32. The significant improvements of the proposed decoder come at the cost of 0.07 dB error-correction performance degradation compared with FSCL-32.
Recently, a generalized successive cancellation list (SCL) decoder implemented with shifted-pruning (SP) scheme, namely the SCL-SP-ω decoder, is presented for polar codes, which is able to shift the pruning window at most ω times during each SCL re-decoding attempt to prevent the correct path from being eliminated. The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs. However, the number of exponential/logarithm operations involved in the SCL-SP-ω decoder grows linearly with the number of information bits and list size, which leads to high computational complexity. In this paper, we present a detailed analysis of the SCL-SP-ω decoder in terms of the decoding performance and complexity, which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously. Then, we introduce a simplified metric derived from the path metric (PM) domain, and a custom-tailored deep learning (DL) network is further designed to enhance the efficiency of the proposed simplified metric. The proposed metrics are both free of transcendental functions and hence, are more hardware-friendly than the existing metrics. Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.