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International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT)

Improved Parity Check Aided Successive Cancellation Flip Polar Decoders

Dwaipayan Ghosh, Sudipta Chattopadhyay

Published Jan 11, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1109/icaect60202.2024.10468728

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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.
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.
When the code length is finite, the successive cancellation list (SCL) decoding of polar codes shows as good error-correction performance as low-density parity-check codes and turbo codes and it will be used in high-speed communications. However, since the hardware complexity of the SCL increases linearly as the size of the list increases, it is difficult to use the high-complexity SCL decoding for devices with limited resource such as IoT devices. The successive cancellation flip (SCF) decoding algorithm has been proposed to solve the problem of high hardware complexity and to enhance the error-correction performance of successive cancellation decoding. However, the conventional SCF decoding has high computational complexity. In this paper, we propose the interleaver-aided successive cancellation flip (ISCF) decoding to reduce the computational complexity. The computational complexity of the ISCF decoding is less by at least 32% than the conventional SCF decoding for error frame at Eb/N0=3.5dB.
Polar codes have garnered significant attention since they were proposed due to their capacity-achieving properties and their low-complexity decoding process, and they were selected as the coding scheme for the control channel in 5G mobile communication technology. A successive cancellation list (SCL) decoder, aided by a cyclic redundancy check (CRC), performs the competitive error correcting performance for polar codes compared to other sophisticated codes. The SCL-Flip decoding algorithm is proposed to enhance the error correction performance of the SCL. However, the SCL-Flip is hampered by a high decoding complexity due to the necessary selection and sorting process of path metrics (PMs). Additionally, it requires a large number of iterations to achieve a good error correction performance. In this paper, we propose the error segment bit-flip (ES-SCL-Flip) decoding algorithm, a simplified bit-flip approach for the SCL decoder based on analyzing the distributions of the first error bit. Firstly, we construct an index set with a high probability of the first erroneous bit. Second, a bit-flip criterion is introduced to prevent the costly operation of the PM selection and sorting without compromising the error correction performance. Finally, a search strategy is employed that utilizes segmented error indication to target and rectify the initial error segment sequentially. The simulation results demonstrate that the ES-SCL-Flip decoder provides an improved error correction performance with only a minimal increase in decoding complexity compared to the conventional CRC-aided SCL decoder. This algorithm attains a commendable equilibrium between the error correction performance and decoding complexity.
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.
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.
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.