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IEEE Transactions on Communications

Improved Successive Cancellation Decoding of Long Polar Codes Through Perturbing a Posteriori LLRs and Its Theoretical Insights

Zhongjun Yang, Li Chen, Xianbin Wang, Huazi Zhang

Published Jan 1, 2026• 2 citations
Publisher

Abstract

For polar codes, perturbing received information can enhance the successive cancellation (SC) decoding performance. This is an effective approach for realizing low-latency yet high performance for long polar codes, since all the perturbation-enhanced SC (PSC) decoding can be performed in parallel. This paper provides theoretical insights into soft information perturbation, revealing that the PSC decoding can be equivalently interpreted as perturbing thea posteriorilog-likelihood ratios (LLRs) of information bits. Such a revelation leads to the design of an improved PSC (IPSC) decoding that yields a lower perturbation complexity. By better utilizing the decodinga posterioriLLRs, a set of possibly erroneous estimations can be formed and further perturbed, resulting in the proposed hybrid PSC (HPSC) decoding. During each new SC decoding attempt, it takes turns to flip the first erroneous bit by introducing a biased perturbation, while the subsequent erroneous estimations are corrected through random perturbations. Our simulation results validate that, for various codeword lengths and rates, the proposed IPSC decoding can achieve a similar performance as the conventional PSC decoding, but yield a significantly reduced perturbation complexity. With the same number of decoding attempts, the proposed HPSC decoding outperforms several state-of-the-art SC-based decoding, such as the thresholded SC-flip (TSCF) decoding and the dynamic SC-flip (DSCF) decoding.

DOI
10.1109/tcomm.2026.3663532

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For polar codes, perturbing received information can enhance the successive cancellation (SC) decoding performance. This is an effective approach for realizing low-latency yet high performance for long polar codes, since all the perturbation-enhanced SC (PSC) decoding can be performed in parallel. This paper provides theoretical insights into soft information perturbation, revealing that the PSC decoding can be equivalently interpreted as perturbing thea posteriorilog-likelihood ratios (LLRs) of information bits. Such a revelation leads to the design of an improved PSC (IPSC) decoding that yields a lower perturbation complexity. By better utilizing the decodinga posterioriLLRs, a set of possibly erroneous estimations can be formed and further perturbed, resulting in the proposed hybrid PSC (HPSC) decoding. During each new SC decoding attempt, it takes turns to flip the first erroneous bit by introducing a biased perturbation, while the subsequent erroneous estimations are corrected through random perturbations. Our simulation results validate that, for various codeword lengths and rates, the proposed IPSC decoding can achieve a similar performance as the conventional PSC decoding, but yield a significantly reduced perturbation complexity. With the same number of decoding attempts, the proposed HPSC decoding outperforms several state-of-the-art SC-based decoding, such as the thresholded SC-flip (TSCF) decoding and the dynamic SC-flip (DSCF) decoding.
For polar codes, perturbing received information can enhance the error-correction performance of successive cancellation (SC) decoding. This is an effective approach for realizing low-latency yet high decoding performance for long polar codes, since each perturbation-enhanced SC (PSC) decoding can be performed in parallel. This paper provides theoretical insights into the soft information perturbation. It first reveals that the PSC decoding can be equivalently viewed as perturbing the SC decoding a posteriori log-likelihood ratio (LLR) of the information bits. Such a revelation enables us to reduce the perturbation complexity by only targeting the information bits, resulting in an improved PSC (IPSC) decoding. By better utilizing the a posteriori LLRs, a set of possibly erroneous estimations can be formed to be perturbed, further reducing the perturbation complexity. Our simulation results show that, for various codeword lengths, the proposed IPSC decoding can achieve a similar performance as the PSC decoding, while yielding significant perturbation complexity reduction.
Soft information perturbations can significantly improve the successive cancellation (SC) decoding performance of polar codes. This is an effective method for realizing low-latency yet high performance for long polar codes, since each perturbation-based SC (PSC) decoding can be performed in parallel. However, little theoretical insight has been revealed so far regarding its work rationale. This paper provides the theoretical analysis of the soft information perturbation. It reveals that PSC decoding improves the SC decoding performance through correcting the erroneous bit estimations, especially the first erroneous bit (FEB). It further validates that perturbing the soft information does not degrade the error-correction capability of SC decoding. Such revelations lead to the design of optimal perturbations that maximizes the FEB correction probability, resulting in an enhanced PSC decoding performance. Based on this, a novel hybrid PSC (HPSC) decoding is proposed. By introducing the random and biased perturbations, the HPSC decoding can better divert from the initial erroneous estimation and converge to the intended one. Our simulation results demonstrate that with the optimal perturbation, the HPSC decoding can achieve a similar performance as the cyclic redundancy check (CRC) aided SC list (CA-SCL) decoding, while avoiding path sorting and expansion.
Soft information perturbation can significantly enhance the successive cancellation list (SCL) decoding performance of polar codes. However, the existing perturbation-based SCL (PSCL) decoding requires a large number of re-decoding attempts, leading to high decoding complexity, and hence limits its application for long polar codes. In this letter, an enhanced PSCL (E-PSCL) decoding is proposed. It utilizes a new biased perturbation strategy that requires a reduced number of redecoding attempts, but yields an advanced decoding performance. To further improve the E-PSCL decoding performance, a reliability metric (RM) is introduced. It can better identify the possibly erroneous positions within the SCL decoding failures. During each decoding attempt, the E-PSCL decoding takes turns to flip these positions. Moreover, for the RM, it is derived from the SCL decoding error probability for which both the frozen bits and the error propagation are considered. Simulation results show that with the same number of decoding attempts, the proposed E-PSCL decoding outperforms the state-of-the-art dynamic SCL flip (D-SCLF) decoding and the conventional PSCL decoding.
In this paper, two decoding algorithms based on Successive-Cancellation (SC) are proposed to improve the error-correction performance of cyclic redundancy check (CRC)-aided polar codes while aiming for a low-complexity implementation. Comparisons with Dynamic SC Flip (DSCF) and SC Perturbation (SCP) are carried out since the proposed DSCF and Perturbation (DSCFP) and Perturbed DSCF (PDSCF) algorithms combine both methods. The analysis includes comparisons with several code lengthsNNNand various number of decoding attemptsTmaxT_{max}Tmax​. ForN=1024N=1024N=1024and the coding rateR=1/2R= 1/2R=1/2, the DSCF and the SCP algorithms withTmax⁡=17T_{\max}= 17Tmax​=17are bested by approximately 0.1 dB at block-error rate (BLER) of 0.001. At BLER = 10−6and forTmax=64T_{max}= 64Tmax​=64, the gain is of 0.375 dB and > 0.5 dB with respect to DSCF and SCP, respectively. At high signal-to-noise ratio, the average computational complexity of the proposed algorithms is virtually equivalent to that of SC.
Polar Codes achieve average error correction performance at finite code lengths, when decoded using Successive Cancellation (SC) decoding. Successive Cancellation Flip (SC-Flip) based decoders provide a viable low complexity substitute of the high performing high complexity Successive Cancellation List (SCL) decoders, providing a considerable improvement in the performance. A novel approach to identify and flip multiple erroneous bits in each decoding attempt has been aimed in this paper. Moreover, a faster version of the proposed decoder is also presented, which provides better performance throughout the entire decoding range. The performance of the proposed decoders have been evaluated with respect to frame error correction rate along with average normalized complexity and then compared with some of the existing works for validating the outperformance.
By adopting successive cancellation list decoding (SCL), polar codes demonstrate competitive error correction performance over LDPC and Turbo codes. However, SCL decoding suffers from high computational complexity and long decoding latency, especially when the list size is very large. Successive cancellation flip (SCF), as another decoding algorithm that can achieve high error correction performance, has a complexity that is close to that of successive cancellation (SC) decoding. With the observation that SCL and SCF decoding are similar at giving more chances to inspect possible codewords simultaneously or sequentially, a novel hybrid decoder is proposed in this paper, which essentially combines the ideas of SCF and SCL decoders. Moreover, in order to compensate for the degradation of performance caused by the reduction of path splitting and further reduce the decoding latency, the convolutional polar codes are adopted with a designed bit-flipping set. Simulation results demonstrate that the proposed decoder achieves the reduction of decoding latency while attaining better performance than conventional CRC-aided SCL decoder.