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IEEE Transactions on Communications

Dynamic-SCFlip Decoding of Polar Codes

Ludovic Chandesris, Valentin Savin, David Declercq

Published Jan 15, 2018• 136 citations
Publisher

Abstract

This paper proposes a generalization of the recently introduced successive cancellation flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard SC decoding. To make such an approach effective, we first introduce the concept of higher order bit flips and propose a new metric to determine the bit flips that are more likely to correct the trajectory of the SC decoding. We then propose a generalized SCFlip decoding algorithm, referred to as dynamic-SCFlip (D-SCFlip), which dynamically builds a list of candidate bit flips, while guaranteeing that the next attempt has the highest probability of success among the remaining ones. Simulation results show that D-SCFlip is an effective alternative to SC-list decoding of polar codes, by providing very good error correcting performance, with an average computation complexity close to the one of the SC decoder.

DOI
10.1109/tcomm.2018.2793887

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Dynamic-SCFlip Decoding of Polar Codes

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International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT)•Jan 11, 2024•1 citation
This paper proposes a generalization of the recently introduced successive cancellation flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard SC decoding. To make such an approach effective, we first introduce the concept of higher order bit flips and propose a new metric to determine the bit flips that are more likely to correct the trajectory of the SC decoding. We then propose a generalized SCFlip decoding algorithm, referred to as dynamic-SCFlip (D-SCFlip), which dynamically builds a list of candidate bit flips, while guaranteeing that the next attempt has the highest probability of success among the remaining ones. Simulation results show that D-SCFlip is an effective alternative to SC-list decoding of polar codes, by providing very good error correcting performance, with an average computation complexity close to the one of the SC decoder.
This paper proposes a generalization of the recently introduced Successive Cancellation Flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard Successive Cancellation (SC) decoding. To make such an approach effective, we first introduce the concept of higher-order bit-flips, and propose a new metric to determine the bit-flips that are more likely to correct the trajectory of the SC decoding. We then propose a generalized SCFlip decoding algorithm, referred to as Dynamic-SCFlip (D-SCFlip), which dynamically builds a list of candidate bit-flips, while guaranteeing that extra decoding attempts are performed by decreasing probability of success. Simulation results show that D-SCFlip is an effective alternative to SC-List decoding of polar codes, by providing very good error correcting performance, with an average computation complexity close to the one of the SC decoder.
Successive cancellation (SC) decoding of polar codes may bring about error propagation that needs to be mitigated. In this paper, we present a new SC Flipping (SCFlip) decoder, named bit error rate (BER) evaluation based SCFlip (BER-SCFlip), which can accurately target the first error bit and correct it with a high probability. Thus, a high error correction capability and a low decoding complexity can be achieved. First, we propose a new criterion to find out the most suspicious error bit. Those non-frozen bits that have higher decoding BERs derived from log-likelihood-ratios (LLRs) after SC decoding than the corresponding expected ones estimated via Gaussian Approximation (GA), are collected into the flip-bits set. These candidate bits will be flipped one by one according to their SC decoding orderings in extra decoding attempts until the decoded codeword passes cyclic redundancy check (CRC) or a predetermined maximum number of extra attempts is reached. We then propose an extended version of BER-SCFlip, named BER-SCFlip-w with the capability to correct up to w error bits in each extra decoding attempt. By combining our criterion for the flip-bits selection with that of Dynamic SCFlip (D-SCFlip), the proposed BER-SCFlip-w significantly reduces decoding complexity and latency while maintaining the superior error-correction performance close to that of D-SCFlip-w. The simulation results show that the proposed schemes are competitive among existing SCFlip algorithms and could achieve the error-correction performance approaching that of CRC-aided SCL decoding under list size L = 16 while maintaining low complexity.
Dynamic successive cancellation flip (D-SCFlip) decoding has emerged as a low-complexity alternative to successive cancellation list (SCL) decoding for polar codes, bridging the performance gap between conventional successive cancellation (SC) and SCL decoding. While D-SCFlip enhances SC decoding with adaptive bit-flip capabilities, its practical efficiency remains constrained by several factors, including the rapid growth of the search space with code dimension, lack of spatial error localization, and uniform resource allocation for correcting bit error decisions. This work presents a complexity-constrained D-SCFlip decoding algorithm that leverages segmented cyclic redundancy check (CRC) as a tool for fine-grained complexity budgeting, enabling dynamic allocation of fixed computational resources based on localized error information. First, we adapt the segmented CRC approach to the D-SCFlip context, replacing the global CRC with localized checks across optimally sized segments to constrain the flip search space to specific error regions. Second, we introduce a computational complexity budgeting mechanism that efficiently allocates decoding resources across segments based on their error susceptibility and correction potential. Our contribution also includes rigorous optimization of segment configuration specifically designed for complexity-constrained decoding. Simulation results demonstrate that our approach achieves better block error rate performance compared to conventional D-SCFlip decoding under equivalent worst-case complexity constraints, with gains of 0.05-0.14 dB across various code rates and lengths.
Polar codes are the first error-correcting codes that achieve the Shannon limit under successive cancellation (SC) decoding when the code length is infinite. However, the error-correcting performance of SC decoding is mediocre for short and moderate code lengths. Dynamic successive cancellation flip (DSCF) decoding has been proposed that performs extra SC decoding trails with multi-bit flipping to improve the performance of short and moderate polar codes. The DSCF decoding suffers from high computational complexity and decoding latency since all information bits are tested when searching for the flipping candidates, which leads to intensive metric calculations. To reduce the search complexity of the DSCF, a method based on the critical set (CS) is proposed in this paper to narrow the search range and two types of special nodes, rate-0 nodes and repetition nodes, are incorporated for further complexity reduction. Simulation results show that the proposed method can achieve more than 70% reduction in calculations on metrics, and up to 22.79% reduction in calculations on nodes without performance loss compared to the original DSCF decoding.
A successive cancellation list (SCL) decoder with the assistance of a cyclic redundancy check (CRC) can provide competitive decoding performance for polar codes compared with the state-of-the-art codes. In this paper, we adopt a bit-flip algorithm for the CRC-assisted SCL decoder to further improve the error-correcting performance. We first introduce a new bit-flip criterion for the SCL decoder. To support this criterion, we give the metric to identify the positions that need to be flipped. To verify the superiority of the proposed bit-flip criterion, we also consider a kind of SCL-flip decoder whose criterion is very similar with the existing one and we will prove that its performance is worse than the decoder with the proposed bit-flip criterion. The simulation results show that the decoder with the proposed bit-flip criterion outperforms both the standard CRC-assisted SCL decoder and the existing SCL-based bit-flip decoder.
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.