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IEEE/CIC International Conference on Communications in China (ICCC)

On the adaptive Fano-SC-Flip Decoding of Polar Codes

Zhenggui Feng, Линг Лиу

Published Aug 11, 2022• 2 citations
Publisher

Abstract

Successive cancellation flip (SCFlip) decoding with flipping characteristic can significantly improve the decoding performance of polar codes by taking the advantage of extra decoding attempts. Therefore, we propose a new Fano-SC-Flip decoding algorithm of polar codes, which integrates the flip feature into the Hybrid (Fano-SC) algorithm. By comparing both the modeling and the genuine complexity, we obtain the applicable conditions where using the Hybrid-Flip decoder is relatively cost-effective with the trade-off between the complexity and error correction performance. Finally, the optimal flip allocation strategy is found and adaptively adjusted for each given SNR, by using the proportion of errors in each segment based on the oracle-assisted SC (OA-SC) decoder.

DOI
10.1109/iccc55456.2022.9880772

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Successive cancellation flip (SCFlip) decoding with flipping characteristic can significantly improve the decoding performance of polar codes by taking the advantage of extra decoding attempts. Therefore, we propose a new Fano-SC-Flip decoding algorithm of polar codes, which integrates the flip feature into the Hybrid (Fano-SC) algorithm. By comparing both the modeling and the genuine complexity, we obtain the applicable conditions where using the Hybrid-Flip decoder is relatively cost-effective with the trade-off between the complexity and error correction performance. Finally, the optimal flip allocation strategy is found and adaptively adjusted for each given SNR, by using the proportion of errors in each segment based on the oracle-assisted SC (OA-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.
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.
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.
The Successive Cancellation decoder cannot provide satisfactory error correcting performance for finite length polar codes. The error performance can be improved by using Successive Cancellation Flip decoders at the expense of higher complexity. In line with this, a novel decoding approach has been developed in this paper, where distributed parity bits are used to divide the codeword into multiple segments having equal probability of error occurrence, allowing early termination. The proposed Segmented Parity Successive Cancellation Flip (SP-SC Flip) Decoder achieves lower normalized complexity and average decoding latency compared to some related existing decoders, without degrading the error correcting performance. Further improvement in decoder performance is observed when code words are divided into a greater number of segments.
There are two main algorithms, successive cancellation (SC) algorithm and brief propagation (BP) algorithm, for decoding polar code. The SC algorithm has better error-correcting performance and the BP algorithm has low latency. The hybrid BP-SC decoding combines these two decoding algorithms and achieves improvements. Furthermore, the successive cancellation flip (SCF) algorithm improves the error-correcting performance for the SC algorithm, but it has higher computation complexity and latency. Based on the hybrid BP-SC decoding, we proposed a hybrid BP-SC/SCF decoding for polar codes in this paper to further improve the error-correcting performance. The result shows our approach outperforms to frame error rates (FER) of the SC decoding and BP decoding at least 0.5-dB and outperforms hybrid BP-SC decoding by 0.2-dB to 0.4-dB. Compared with the SCF decoding, the hybrid BPSC/SCF decoding has a small degradation of FER in a highquality channel but it significantly reduces the average computation complexity.
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.