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.
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 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.
The eBCH-polar codes is a powerful way to construct polar codes. With high minimum Hamming distance, it outperforms ordinary Polar codes under successive cancellation list (SCL) decoder. However, the absence of cyclic redundancy check (CRC) bits in eBCH-polar codes makes it challenging to adopt SCL-flip (SCLF) decoding scheme. In this research, we propose a flip scheme activated by a Normalized Path Metric (PM) range and a mismatch criterion, which respectively leverage the properties of SCL decoding and dynamic frozen bits of eBCH-polar codes. This work also improves the selection the flipping bits by modifying metric to account for the structure of dynamic frozen bits and reduce the search space. Based on these modifications, we proposed SCLF-1 and SCLF-2 decoding algorithms for eBCH-polar codes. Simulation results show that both of the proposed decoding schemes achieve superior performance compared to other contemporary decoding algorithms for CRC aided polar (CA-polar) codes, demonstrating enhanced error rates performance within the same decoding attempt.
Novel successive cancellation list (SCL) decoding schemes of Polar codes by exploiting the error correction (EC) capability of the cyclic redundancy check (CRC) codes are proposed in this paper. Different from the schemes in the literature that only considered the error detection capability of CRC, the proposed schemes aim to improve the performance of CRC-aided Polar decoding to the most by benefiting from the potential EC capability of CRC. Specifically, we first propose a basic decoding scheme, named CRC error-correction-aided successive cancellation list (CRC-EC-SCL) decoding, by introducing the look-up-table-based CRC EC method into the Polar SCL decoding process. Then, based on the basic scheme, we further propose the segmented-CRC-EC-SCL decoding scheme. By segmented-CRC, the information block is divided into multiple segments and each segment is attached with a shorter CRC sequence. By conducting the CRC-EC-aided coding for each of the segments, multiple erroneous bits can be corrected early and error propagation can, thus, be efficiently suppressed. The simulation results show that both of the proposed decoding schemes have a significant performance gain over the classic CRC-EC-SCL decoding scheme. Especially for the segmented-CRC-EC-SCL, the performance gain at a frame error rate of 10−4is about 0.4 dB. Moreover, the average computation complexity of the segmented-CRC-EC-SCL is close to the classic scheme.
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.
A deep-learning-aided successive-cancellation list (DL-SCL) decoding algorithm for polar codes is introduced with deep-learning-aided successive-cancellation (DL-SC) decoding being a specific case of it. The DL-SCL decoder works by allowing additional rounds of SCL decoding when the first SCL decoding attempt fails, using a novel bit-flipping metric. The proposed bit-flipping metric exploits the inherent relations between the information bits in polar codes that are represented by a correlation matrix. The correlation matrix is then optimized using emerging deep-learning techniques. Performance results on a polar code of length 128 with 64 information bits concatenated with a 24-bit cyclic redundancy check show that the proposed bit-flipping metric in the proposed DL-SCL decoder requires up to 66% fewer multiplications and up to 36% fewer additions, without any need to perform transcendental functions, and by providing almost the same error-correction performance in comparison with the state of the art.
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.