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International Conference on Signal Processing

Repeated-Part Adaptive Successive Cancellation List Decoder for Polar Codes with Cyclic Redundancy Check

Yansong Lv, Jianping Li, Man Hu

Published Aug 1, 2018• 0 citations
Publisher

Abstract

Compared with the conventional SC-List decoder, adaptive SC-List decoder can achieve similar performance but with significantly average complexity reduce. Based on the implementation of adaptive SC-List decoder, we found a phenomenon in simulation that when the adaptive L is less than or equal to 4, there is no small probability to get the first candidate path through CRC. For the phenomenon, we proposed a repeated-part adaptive SC-List decoder, which repeat the decoding process when the value of adaptive L (searching width) is less than or equal to 4. Simulation results show that the new decoder can significantly reduce the complexity of AD-SCL algorithm with not obvious bit error rate performance improvement.

DOI
10.1109/icsp.2018.8652469

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Compared with the conventional SC-List decoder, adaptive SC-List decoder can achieve similar performance but with significantly average complexity reduce. Based on the implementation of adaptive SC-List decoder, we found a phenomenon in simulation that when the adaptive L is less than or equal to 4, there is no small probability to get the first candidate path through CRC. For the phenomenon, we proposed a repeated-part adaptive SC-List decoder, which repeat the decoding process when the value of adaptive L (searching width) is less than or equal to 4. Simulation results show that the new decoder can significantly reduce the complexity of AD-SCL algorithm with not obvious bit error rate performance improvement.
Although the adaptive successive cancellation list (AD-SCL) algorithm and the segmented-CRC adaptive successive cancellation list (SCAD-SCL) algorithm based on the cyclic redundancy check (CRC) can greatly reduce the computational complexity of the successive cancellation list (SCL) algorithm, these two algorithms discard the previous decoding result and re-decode by increasing L, where L is the size of list. When CRC fails, these two algorithms waste useful information from the previous decoding. In this paper, a simplified adaptive successive cancellation list (SAD-SCL) is proposed. Before the re-decoding of updating value L each time, SAD-SCL uses the existing log likelihood ratio (LLR) information to locate the range of burst error bits, and then re-decoding starts at the incorrect bit with the smallest index in this range. Moreover, when the segmented information sequence cannot get the correct result of decoding, the SAD-SCL algorithm uses SC decoding to complete the decoding of the subsequent segmentation information sequence. Furthermore, its decoding performance is almost the same as that of the subsequent segmentation information sequence using the AD-SCL algorithm. The simulation results show that the SAD-SCL algorithm has lower computational complexity than AD-SCL and SCAD-SCL with negligible loss of performance.
Cyclic redundancy check (CRC)-aided successive cancellation list (CA-SCL) decoding algorithm has brought good error performance. Recently, some researchers utilized multiple CRC codes to reduce decoding complexity of CA-SCL decoding algorithm. However, based on CA-SCL decoding frame, we not only reduce decoding complexity but also improve error performance. We divide polar codeword into independent sub-blocks during the process of encoding. Meanwhile, locations of multiple CRC are optimized according to a value of each average Bhattacharyya parameter. Finally, for CA-SCL decoding, results indicate that our constructed polar codes show an admirable error performance and low decoding complexity than that of equal sub-block codewords.
Combined with cyclic redundancy check (CRC), SC list (SCL) decoder can achieve outstanding error correction performance, which is more obvious with increasing list size. However, the corresponding decoding complexity and latency increase with the list size. To this end, the selection of list size becomes essential for practical applications. A new artificial neural network (ANN) based framework is proposed in this paper to design a hardware-friendly adaptive SCL (DL-ASCL) decoder. First, the list size at each stage is predicted by an ANN predictor. The performance achieved based on the proposed DL-ASCL algorithm is close to the optimal SCL decoder with the same list size, especially in the high signal-to-noise ratio (SNR) region. Meanwhile, the computational complexity is significantly reduced compared with the conventional ones. Numerical results have demonstrated that the proposed deep learning based adaptive SCL decoder can achieve 56% computational complexity reduction compared with the conventional SCL decoder for the polar code with length 128 and rate 1/2. The hardware architecture of the adaptive SCL decoder based on the predicted list size is proposed and the folding technique is also adopted, which helps reduce the hardware cost by about 25%.
An improved CA-SCL (CRC-Aided Successive Cancellation List) decoding algorithm for Polar codes is proposed in this paper. By introducing the global cyclic redundancy check and local parity check, a lower bit error rate is obtained comparing with the known results. The new algorithm constructs a prune decoding path by the parity check in the local processing. Since the parity check can only detect an odd number of errors, the global CRC is used to increase the error detection ability and the decoding accuracy. The performance of the improved decoding algorithm is better than the known results, especially when the code length is either less than or equal to 512, and the code rate is not greater than 0.5 in case of the signal-to-noise ratio (SNR) higher than 3dB. In particular, when the code length is 256 with code rate of 0.5 and decoding list size of 32 under the condition of bit error rate 10-5on the AWGN channel, the proposed algorithm has around 0.25dB and 0.55dB performance gain comparing with that of the CA-SCL and SCL algorithms, respectively.
In order to make a better trade-off between computational complexity and decoding performance, a cyclic redundancy check (CRC)-aided split-reduced successive cancellation list (CA-SR-SCL) algorithm is proposed in this paper. Based on the splitting rule defined in split-reduced SCL (SR-SCL) algorithm and enhanced-SR-SCL (ESR-SCL) algorithm, the splitting characteristics of the correct decoding path are calculated. In addition, a new pruning rule is proposed to timely delete the candidate paths that split frequently, and a CRC detector is appended to improve the error correction performance. Compared to the ESR-SCL algorithm, simulation results demonstrate that the proposed algorithm can achieve better performance with lower computational complexity.
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.