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IEEE International Conference on Digital Signal Processing (DSP)

BP Polar Decoders with Early Termination and Belief Enhancing

Chao Yang, Junmei Yang, Xiao Liang, Zaichen Zhang, Xiaohu You, Chuan Zhang

Published Nov 1, 2018• 5 citations
Publisher

Abstract

In this paper an early termination scheme, partial LLR-aided (PLA) scheme, is proposed for belief propagation (BP) polar decoding with lower complexity and higher throughput. Numerical results of (1024, 512) code show at least 82% iteration reduction than conventional design at SNR =3.5 dB with proposed early termination scheme. In this paper, belief enhancing schemes based on threshold and cyclic redundancy check (CRC) are proposed, namely, threshold-based LLR (TB-LLR) scheme and segment-divided CRC (SD-CRC) scheme. For (1024, 512) polar code, the performance gains for TB-LLR and SD-CRC are 0.35 dB and 0.2 dB respectively, when BER = 10-3. A general hardware architecture for proposed BP polar decoders is also proposed.

DOI
10.1109/icdsp.2018.8631617

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In this paper an early termination scheme, partial LLR-aided (PLA) scheme, is proposed for belief propagation (BP) polar decoding with lower complexity and higher throughput. Numerical results of (1024, 512) code show at least 82% iteration reduction than conventional design at SNR =3.5 dB with proposed early termination scheme. In this paper, belief enhancing schemes based on threshold and cyclic redundancy check (CRC) are proposed, namely, threshold-based LLR (TB-LLR) scheme and segment-divided CRC (SD-CRC) scheme. For (1024, 512) polar code, the performance gains for TB-LLR and SD-CRC are 0.35 dB and 0.2 dB respectively, when BER = 10-3. A general hardware architecture for proposed BP polar decoders is also proposed.
Belief propagation (BP) is an iterative and parallel decoding algorithm for polar code that satisfies high throughput and low latency requirements in 5G scenarios. In this work, we proposed a cyclic redundancy check aided belief propagation decoding with the box and match algorithm (CBP-BMA) to enhance the error-correction performance further. This algorithm first runs the BP decoder with early stopping criteria and then uses the soft decoded BP log-likelihood ratio (LLR) as the soft input to the box and match algorithm (BMA) decoder. The simulation results show that even if the reprocessing order of the BMA decoder is as low as one, the proposed algorithm shows a significant improvement than BP decoding. With code rate R=0.5 and code length N=128, the suggested algorithm has a gain of roughly 0.3dB at the desired bit error rate (BER) of 10–3.
This paper proposes a novel iterative decoder based on concatenated belief propagation (BP) for CRC-aided polar codes. Compared to the conventional BP-based decoders for polar codes, soft cancellation (SCAN) decoder can generate a log likelihood ratio (LLR) of coded bit with lower computational complexity without sacrificing the detection capability. Unfortunately, its performance is not as good as that of CRC-aided successive cancellation list decoder (SCLD) although SCAN decoder has advantage of hardware implementation. To compensate the performance gap, we exploit CRC structure for not only error detection but also error correction with the assistance of its error correction capability at a short code length by exchanging LLRs between SCAN decoder and BP decoder on the basis of CRC. Moreover, the sub-optimal criterion for selecting a parity check matrix of CRC for BP decoder is proposed. Finally, computer simulations are conducted to confirm the validity of our proposed method. The proposed method can obtain the gain of about 0.6 dB at BER=10-3compared to the native SCAN decoder without requiring huge memory size as in SCLD.
Due to the design principle of parallel processing, belief propagation (BP) decoding is attractive, and it provides good error-correction performance compared with successive cancellation (SC) decoding. However, its error-correction performance is still inferior to that of successive cancellation list (SCL) decoding. Consequently, this paper proposes a novel flip-list- (FL)-enabled belief propagation (BP) method to improve the error-correction performance of BP decoding for polar codes with low computational complexity. The proposed technique identifies the vulnerable channel log-likelihood ratio (LLR) that deteriorates the BP decoding result. The FL is utilized to efficiently identify the erroneous channel LLRs and correct them for the next BP decoding attempt. The preprocessed channel LLR through FL improves the error-correction performance with minimal flipping attempts and reduces the computational complexity. The proposed technique was compared with the state-of-the-art BP, i.e., BP bit-flip (BP-BF), generalized BP-flip (GBPF), cyclic redundancy check (CRC)-aided (CA-SCL) decoding, and ordered statistic decoding (OSD), algorithms. Simulation results showed that the FL-BP had an excellent block error rate (BLER) performance gain up to 0.7 dB compared with BP, BP-BF, and GBPF decoder. Besides, the computational complexity was reduced considerably in the high signal-to-noise ratio (SNR) regime compared with the BP-BF and GBPF decoding methods.
Abstract In this letter, a modified message passing algorithm to prevent short cycles in the factor graph is proposed and combined with a relaxation technique to improve the performance of cyclic redundancy check aided belief propagation decoding for polar codes. Numerical results show that the proposed scheme can achieve a 0.7 dB coding gain, for the code rate of 0.5 at the block error rate of 10 −5 with a comparable average number of iterations over the pure belief propagation decoding scheme when the code block length is 1024.
In this paper, a belief propagation (BP) decoding algorithm with early termination is proposed for polar code. The early termination is accomplished using the syndrome generated by the parity-check matrix, which can be transferred from the generator matrix. With the assistance of the early termination, the BP decoder can provide not only a better bit error rate performance but also significantly reduce the decoding complexity. For (1024, 512) polar codes, the average numbers of iterations can be reduced from 80 to 23 when Eb/N0=3 dB. The reduction in the computation complexity is about 70%.
It has been shown that the permutation factor graph is an effective method to improve the performance of belief propagation (BP) decoding. The research of belief propagation list (BPL) algorithm based on permutation factor graph has also made great progress, but the complexity of decoding process is still too high. In order to compromise performance and complexity, in this work, we focus on the iterative convergence of BPL decoding algorithm, and propose an early termination BPL algorithm based on multiple CRCs. The results show that the improved BPL decoding scheme can provide higher throughput and achieve similar decoding performance with the existing BPL decoding under the same simulation condition.