Guessing random additive noise decoding (GRAND) is a recently proposed decoding algorithm which can achieve the error performance of maximum likelihood (ML) decoding. However, GRAND and its variants are only suitable for some short codes with high code rates and have large average query numbers. To mitigate these problems, we propose a successive cancellation list (SCL)-GRAND decoding algorithm for the cyclic redundancy check concatenated polar (CRC-polar) codes. The proposed decoder first divides the received sequence into two subblocks. Then SCL is used to decode the upper subblock and output several candidates into the candidate list. For each candidate, GRAND is used to decode the lower subblock and finally choose the most-likely codeword as the decoded result. Since the SCL is integrated into the SCL-GRAND algorithm, this algorithm can achieve lower complexity and better flexibility than the original GRAND.
Guessing random additive noise decoding (GRAND) is a recently proposed decoding algorithm which can achieve the error performance of maximum likelihood (ML) decoding. However, GRAND and its variants are only suitable for some short codes with high code rates and have large average query numbers. To mitigate these problems, we propose a successive cancellation list (SCL)-GRAND decoding algorithm for the cyclic redundancy check concatenated polar (CRC-polar) codes. The proposed decoder first divides the received sequence into two subblocks. Then SCL is used to decode the upper subblock and output several candidates into the candidate list. For each candidate, GRAND is used to decode the lower subblock and finally choose the most-likely codeword as the decoded result. Since the SCL is integrated into the SCL-GRAND algorithm, this algorithm can achieve lower complexity and better flexibility than the original GRAND.
Maximum Likelihood (ML) decoding of forward error correction codes is known to be optimally accurate, but is not used in practice as it proves too challenging to efficiently implement. Here we propose a development of a previously described hard detection ML decoder called Guessing Random Additive Noise Decoding (GRAND). We introduce Soft GRAND (SGRAND), a ML decoder that fully avails of soft detection information and is suitable for use with any arbitrary high-rate, short-length block code. We assess SGRAND's performance on Cyclic Redundancy Check (CRC)-aided Polar (CA-Polar) codes, which will be used for all control channel communication in 5G New Radio (NR), comparing its accuracy with CRC-Aided Successive Cancellation List decoding (CA-SCL), a state-of-the-art soft-information decoder specific to CA-Polar codes.
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.
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.
CRC codes have long since been adopted in a vast range of applications. The established notion that they are suitable primarily for error detection can be set aside through use of the recently proposed Guessing Random Additive Noise Decoding (GRAND). Hard-detection (GRAND-SOS) and soft-detection (ORBGRAND) variants can decode any short, high-rate block code, making them suitable for error correction of CRC-coded data. When decoded with GRAND, short CRC codes have error correction capability that is at least as good as popular codes such as BCH codes, but with no restriction on either code length or rate.The state-of-the-art CA-Polar codes are concatenated CRC and Polar codes. For error correction, we find that the CRC is a better short code than either Polar or CA-Polar codes. Moreover, the standard CA-SCL decoder only uses the CRC for error detection and therefore suffers severe performance degradation in short, high rate settings when compared with the performance GRAND provides, which uses all of the CA-Polar bits for error correction.Using GRAND, existing systems can be upgraded from error detection to low-latency error correction without re-engineering the encoder, and additional applications of CRCs can be found in IoT, Ultra-Reliable Low Latency Communication (URLLC), and beyond. The universality of GRAND, its ready parallelized implementation in hardware, and the good performance of CRC as codes make their combination a viable solution for low-latency applications.
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.