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Optoelectronics Letters

Simplified SCL decoding algorithm of polar codes based on critical sets

Jianguo Yuan, Fengguo Zhang, Jingjie He, Sheng Huang

Published Jun 1, 2023• 3 citations
Publisher
DOI
10.1007/s11801-023-2164-4

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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.
This work focuses on further reducing the decoding latency of the successive cancellation list (SCL) algorithm for polar codes, considering the fact that some path splitting may be unnecessary if a bit is reliable during the transmission. Specifically, during the node-wise SCL decoding progress, only unreliable bits need to conduct path clone, leading to the reduction of the number of path splitting and the decoding latency. On this basis, this paper proposes an improved simplified SCL (SSCL) algorithm and an improved Fast-SCL (FSCL) algorithm, for low-latency polar decoding. Simulation results performed on a (4096, 2048) polar code show that the improved SSCL algorithm reduces the decoding latency by around 44.7% when L = 4, and by 62.8% when L = 8, respectively. Moreover, the improved FSCL algorithm achieves a reduction of decoding latency by about 37.3% when L = 8, for a (4096, 3840) polar code.