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Journal of Physics Conference Series

Efficient Construction of Successive Cancellation Decoding of Polar Codes using Logistic regression Algorithm

A. Albert Raj, David Judson, A. Beno

Published Aug 1, 2021• 6 citations
Publisher

Abstract

Abstract In recent days, polar codes have attracted the attention of Industry and Academia. It is one of a linear block error correction codes. Polar codes are one of the capacity achieving algorithms over a wide range of channels, making them very attractive from a theoretical perspective. Polar codes are shown to be instances of concatenated codes. It has been shown that the effect of a polar code can be enhanced by showing the multistage decoding algorithm with log-likelihood based Successive List decoding (SCL). However, SCL decoders are no longer optimal in terms of frame error rate. It is believed that the machine learning based algorithm can improve the FER for the decoded bit. Thus, the logistic regression algorithm is proposed in this paper. The proposed method offers an optimized solution to the decoded bits. The simulation result shows that with sufficient training, this method can provide a lower frame error rate for different code lengths.

DOI
10.1088/1742-6596/1998/1/012010

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Abstract In recent days, polar codes have attracted the attention of Industry and Academia. It is one of a linear block error correction codes. Polar codes are one of the capacity achieving algorithms over a wide range of channels, making them very attractive from a theoretical perspective. Polar codes are shown to be instances of concatenated codes. It has been shown that the effect of a polar code can be enhanced by showing the multistage decoding algorithm with log-likelihood based Successive List decoding (SCL). However, SCL decoders are no longer optimal in terms of frame error rate. It is believed that the machine learning based algorithm can improve the FER for the decoded bit. Thus, the logistic regression algorithm is proposed in this paper. The proposed method offers an optimized solution to the decoded bits. The simulation result shows that with sufficient training, this method can provide a lower frame error rate for different code lengths.
Polar codes have been selected as the channel coding scheme for the Enhanced Mobile Broadband (eMBB) control channel in 5G, which requires short length codes. One of the main challenges in utilizing polar codes is the design of low-complexity decoders with adequate error-correcting performance. The Successive Cancellation (SC) decoder was introduced as the first algorithm enabling polar codes to achieve the channel capacity for long codelengths. However, for shorter codelengths, this decoder does not provide satisfactory error-correction performance. To address this limitation, the Successive Cancellation List (SCL) decoder has been proposed, which performs decoding by maintaining a list of candidate paths and selecting the best one based on a path metric. In this paper, we propose improving the error-correction performance of the SCL decoder using concatenated Cyclic Redundancy Check (CRC) codes and Long Short-Term Memory (LSTM) network. Simulation results demonstrate that the proposed method outperforms the Belief Propagation (BP) decoder in terms of Bit Error Rate (BER) curves. Furthermore, the accuracy of the LSTM model in this study improves from 73 percent in previous research to 93.77 percent.
Although original successive cancellation flip (SCF) decoding of the polar codes can identify the first error position and flip the error, decoding still fails when other errors occur after the corrected error bit. Therefore, the improvement of the block error rate (BLER) performance is limited. In this paper, we present an improved algorithm that can correct multiple error bits, named as improved multiple bit-flipping successive cancellation decoding algorithm. First, multiple sets are constructed by calculating the log likelihood ratio (LLR) of each information bit. Then, a bit is selected and corrected from the first set when original decoding fails; two bits are selected and flipped from the second set when all bits in the first set cannot be successfully decoded; when all bits combinations in the second set are flipped but the output vector still does not match the input vector, three bits are selected and corrected from the third set. Simulation results show that the BLER performance of the improved algorithm is better than that of the successive cancellation list decoding (SCL) decoding algorithm with a list size of L = 8 for N = 256. When N = 1024 and SNR = 3 dB, the BLER performance of improved algorithm is slightly better than that of SCL decoding algorithm with a list size of L = 4.
Successive cancellation list (SCL) decoding algorithm is a powerful method that can help polar codes achieve excellent error-correcting performance. However, the current SCL algorithm and decoders are based on likelihood or log-likelihood forms, which render high hardware complexity. In this paper, we propose a log-likelihood-ratio (LLR)-based SCL (LLR-SCL) decoding algorithm, which only needs half the computation and storage complexity than the conventional one. Then, based on the proposed algorithm, we develop low-complexity VLSI architectures for LLR-SCL decoders. Analysis results show that the proposed LLR-SCL decoder achieves 50% reduction in hardware and 98% improvement in hardware efficiency.
Facing the challenge of enormous data sets variety, several machine learning-based algorithms for prediction (e.g, Support vector machine, multi layer perceptron and logistic regression) have been highly proposed and used over the last years in many fields. Error correcting codes (ECCs) are extensively used in practice to protect data against damaged data storage systems and against random errors due to noise effects. In this paper, we will use machine learning methods, especially multi-class logistic regression combined with the famous syndrome decoding algorithm. The main idea behind our decoding method which we call logistic regression decoder (LRDec) is to use the efficient multi-class logistic regression models to find errors from syndromes in linear codes such as bose, ray-chaudhuri and hocquenghem (BCH), and the quadratic residue (QR). Obtained results of the proposed decoder have a significant benefit in terms of bit error rate (BER) for random binary codes. The comparison of our decoder with many competitors proves its power. The proposed decoder has reached a success percentage of 100% for correctable errors in the studied codes.
Polar codes are capacity achieving error correcting codes that can be decoded through the successive-cancellation algorithm. To improve its error-correction performance, a list-based version called successive-cancellation list (SCL) has been proposed in the past, that however substantially increases the number of time-steps in the decoding process. The simplified SCL (SSCL) decoding algorithm exploits constituent codes within the polar code structure to greatly reduce the required number of time-steps without introducing any error-correction performance loss. In this paper, we propose a faster decoding approach to decode one of these constituent codes, the Rate-1 node. We use this Rate-1 node decoder to develop Fast-SSCL. We demonstrate that only a list-size-bound number of bits needs to be estimated in Rate-1 nodes and Fast-SSCL exactly matches the error-correction performance of SCL and SSCL. This technique can potentially greatly reduce the total number of time-steps needed for polar codes decoding: analysis on a set of case studies show that Fast-SSCL has a number of time-steps requirement that is up to 66.6% lower than SSCL and 88.1% lower than SCL.
Polar codes are capacity achieving error correcting codes that can be decoded through the successive-cancellation algorithm. To improve its error-correction performance, a list-based version called successive-cancellation list (SCL) has been proposed in the past, that however substantially increases the number of time-steps in the decoding process. The simplified SCL (SSCL) decoding algorithm exploits constituent codes within the polar code structure to greatly reduce the required number of time-steps without introducing any error-correction performance loss. In this paper, we propose a faster decoding approach to decode one of these constituent codes, the Rate-1 node. We use this Rate-1 node decoder to develop Fast-SSCL. We demonstrate that only a list-size-bound number of bits needs to be estimated in Rate-1 nodes and Fast-SSCL exactly matches the error-correction performance of SCL and SSCL. This technique can potentially greatly reduce the total number of time-steps needed for polar codes decoding: analysis on a set of case studies show that Fast-SSCL has a number of time- steps requirement that is up to 66.6% lower than SSCL and 88.1% lower than SCL.