Polar codes represent one of the major breakthroughs in 5G standard, and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list (SCL) decoding algorithm.However, the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check (CRC) polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.
Polar codes represent one of the major breakthroughs in 5G standard, and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list (SCL) decoding algorithm.However, the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check (CRC) polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.
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.
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.
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.
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.
We investigate the cyclic redundancy check (CRC) codes aided successive cancellation list (SCL) decoding schemes to improve the performance of Polar codes. Distinguished from the existing literatures of Polar codes that only consider the error detection capability of CRC, we attempt to take advantage of the inherent error correction capability of CRC and we first devise a segmented CRC-error-correcting aided SCL decoding (SCC-SCL) framework. Based on this framework, an error-correcting table based SCC-SCL (ET-SCC-SCL) decoding scheme is proposed, by introducing the look-up-table based CRC error correction method into the segmented Polar SCL decoding process. Since the error correction capability is limited by the size of the look-up table, which in turn limits the performance gain, we further propose a deep learning based SCC-SCL (DL-SCC-SCL) decoding scheme. In this scheme, a long short-term memory (LSTM) network replaces the error correction table to perform error correction, combining the sequence of log likelihood ratios (LLRs) with the syndromes to determine the error patterns. Simulation results show that both of the proposed decoding schemes have significant performance gain over the classic CRC error-detection aided SCL decoding scheme. Especially for the DL-SCC-SCL, the performance gain at bit error rate of 10-5is about 0.5 dB.
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.