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IEEE Communications Letters

Enhanced List Decoding of Long Polar Codes Through Efficient Perturbation

Zhongjun Yang

Published Jan 1, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1109/lcomm.2026.3674547

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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.
The eBCH-polar codes is a powerful way to construct polar codes. With high minimum Hamming distance, it outperforms ordinary Polar codes under successive cancellation list (SCL) decoder. However, the absence of cyclic redundancy check (CRC) bits in eBCH-polar codes makes it challenging to adopt SCL-flip (SCLF) decoding scheme. In this research, we propose a flip scheme activated by a Normalized Path Metric (PM) range and a mismatch criterion, which respectively leverage the properties of SCL decoding and dynamic frozen bits of eBCH-polar codes. This work also improves the selection the flipping bits by modifying metric to account for the structure of dynamic frozen bits and reduce the search space. Based on these modifications, we proposed SCLF-1 and SCLF-2 decoding algorithms for eBCH-polar codes. Simulation results show that both of the proposed decoding schemes achieve superior performance compared to other contemporary decoding algorithms for CRC aided polar (CA-polar) codes, demonstrating enhanced error rates performance within the same decoding attempt.
Polar codes, as the coding scheme for the control channel in fifth-generation mobile communication technology (5G), have attracted widespread attention since their proposal. As a mainstream decoding algorithm for polar codes, the successive cancellation list (SCL) decoder usually improves the error correction performance by increasing the list size, but this method suffers from the problems of high decoding complexity. To address this problem, this paper proposes a layered-search bit-flipping (LS-SCLF) decoding algorithm based on SCL decoding. Firstly, a new flip-bit metric is proposed, which derives a formula to approximate the probability of an error occurring in an information bit. This formula introduces a perturbation parameter to improve the calculation accuracy. Secondly, a compromise scheme for determining the perturbation parameter is proposed. The scheme uses Monte Carlo simulation to determine an optimized parameter for the precise positioning of the first erroneous decoded bit under different decoding conditions. Finally, a layered search strategy is adopted to sequentially search the erroneous decoded bits from the low order to high order, which can correct up to multiple bits at the same time. Simulation results show that the proposed algorithm achieves improved error correction performance with a slight increase in decoding complexity compared to the generalized SCL-Flip (GSCLF) decoding algorithm. This algorithm also achieves a good balance between the error correction performance and decoding complexity.
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, successive cancellation list (SCL) decoding algorithm significantly improves finite-length performance compared to SC decoding. SCL-flip decoding can further enhance the performance but the gain diminishes as code length increases, due to the difficulty in locating the first error bit position. In this work, we introduce an SCL-perturbation decoding algorithm to address this issue. A basic version of the algorithm introduces small random perturbations to the received symbols before each SCL decoding attempt, and exhibits non-diminishing gain at large block lengths. Its enhanced version adaptively performs random perturbations or directional perturbation on each received symbol according to previous decoding results, and managed to correct more errors with fewer decoding attempts. Extensive simulation results demonstrate stable gains across various code rates, lengths and list sizes. To the best of our knowledge, this is the first SCL enhancement with non-diminishing gains as code length increases, and achieves unprecedented efficiency. With only one additional SCL-LLL decoding attempt (in total two), the proposed algorithm achieves SCL-2L2L2L-equivalent performance. Since the gain is obtained without increasing list size, the algorithm is best suited for hardware implementation.
Successive cancellation list (SCL) decoding enables polar codes and their generalizations to deliver satisfactory performance in finite-length scenarios but it comes with high latency and complexity. To reduce latency, a partitioned SCL (PSCL) decoding algorithm, implemented over a PSCL decoding tree, can be utilized. In this work, we aim to lower down the complexity of the PSCL decoding, resulting in an efficient decoding algorithm with low latency and complexity for polar-like codes. To achieve this, we define two metrics at each level of the PSCL decoding tree. One is for evaluating the reliability of a path and the other is for estimating the probability of the correct path being included in a list of paths. Then, we propose a double-threshold strategy in the PSCL decoding process where unreliable valid paths are pruned based on the first metric, and then a list of surviving paths is selected based on the second metric. Simulation results demonstrate that when polar/CRC-polar/PAC codes are decoded using the proposed low-complexity PSCL decoder, both the sorting complexity and the computational complexity are reduced and significantly decrease as the signal-to-noise ratio (SNR) increases.
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.