A two-part successive syndrome-check decoding of polar codes is proposed with the first part successively refining the received codeword and the second part checking its syndrome. A new formulation of the successive-cancellation (SC) decoding algorithm is presented that allows for successively refining the received codeword by comparing the log-likelihood ratio value of a frozen bit with its predefined value. The syndrome of the refined received codeword is then checked for possible errors. In case there are no errors, the decoding process is terminated. Otherwise, the decoder continues to refine the received code-word. The proposed method is extended to the case of SC list (SCL) decoding by terminating the decoding process when the syndrome of the best candidate in the list indicates no errors. Simulation results show that the proposed method reduces the time-complexity of SC and SCL decoders and their fast variants, especially at high signal-to-noise ratios.
A two-part successive syndrome-check decoding of polar codes is proposed with the first part successively refining the received codeword and the second part checking its syndrome. A new formulation of the successive-cancellation (SC) decoding algorithm is presented that allows for successively refining the received codeword by comparing the log-likelihood ratio value of a frozen bit with its predefined value. The syndrome of the refined received codeword is then checked for possible errors. In case there are no errors, the decoding process is terminated. Otherwise, the decoder continues to refine the received code-word. The proposed method is extended to the case of SC list (SCL) decoding by terminating the decoding process when the syndrome of the best candidate in the list indicates no errors. Simulation results show that the proposed method reduces the time-complexity of SC and SCL decoders and their fast variants, especially at high signal-to-noise ratios.
Successive cancellation (SC) decoding algorithm and successive cancellation list (SCL) decoding algorithm are two common decoding methods for polar codes. The SC decoding algorithm has low complexity, but in its decoding process, the bits with small channel indices are used to assist the decoding of the bits with large channel indices. Therefore, the bit being decoded depends on the bits that have already been decoded which causes error propagation. On the basis of SC decoding, the SCL decoding algorithm overcomes the problem of error propagation by widening the path search width and retaining multiple paths at the same time in the decoding process. However, the complexity of SCL decoding is higher than that of SC decoding. Without changing the performance of the SCL decoding algorithm, we propose a low-complexity SCL decoding algorithm based on path metric (PM). After the last frozen bit is decoded, the path with the smallest PM is selected, and the subsequent nodes adopt SC decoding. Through this combination of SCL decoding and SC decoding, the complexity of the SCL decoding algorithm can be effectively reduced while the SCL decoding performance remains unchanged, especially in the case of high code rates.
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 are the first provably capacity-achieving novel channel codes. Successive cancellation list (SCL) decoding algorithm has a performance close to maximum-likelihood decoding when code length is finite, though the complexity is high. To reduce the complexity of SCL, a partial path expansion with segmented check and pruning SCL (PPE-SCP-SCL) algorithm is proposed in this paper. Based on the successive decoding structure, if the decoding result of a bit is judged to be reliable enough, then a hard decision is made directly and no path expansion is necessary. Moreover, several parity-check points are introduced to perform segmented parity-check during the decoding process, and if the check fails, the current path is directly abandoned. The rationality of the operations is theoretically verified, and numerical simulations also verify that the proposed algorithm can significantly reduce the complexity of decoding with trivial loss of error performance.
Successive cancellation list (SCL) decoding algorithm is a powerful method that can help polar codes achieve excellent error-correcting performance. However, the current SCL algorithm and decoders are based on likelihood or log-likelihood forms, which render high hardware complexity. In this paper, we propose a log-likelihood-ratio (LLR)-based SCL (LLR-SCL) decoding algorithm, which only needs half the computation and storage complexity than the conventional one. Then, based on the proposed algorithm, we develop low-complexity VLSI architectures for LLR-SCL decoders. Analysis results show that the proposed LLR-SCL decoder achieves 50% reduction in hardware and 98% improvement in hardware efficiency.
The authors propose a low complexity list successive cancellation (LCLSC) decoding algorithm, where the advantages of the successive cancellation (SC) decoding and the list successive cancellation (LSC) decoding are both considered. In the proposed decoding, SC decoding instead of LSC decoding is implemented when all information bits from bad subchannels are received reliably. While the reliability of each information bit is estimated by its likelihood ratio (LR), the bit channel quality is measured via its Bhattacharyya parameter. To achieve this goal, the authors introduce two thresholds: LR threshold and Bhattacharyya parameter threshold. Also, the methods to determine them are both elaborated. The numerical results suggest that the complexity of LCLSC decoding is much lower than LSC decoding and can be close to that of SC decoding, while the error performance is almost equal to that of LSC decoding. Especially, when the code rate is in low region, the advantage of our decoding is more obvious.
Polar codes have emerged as a focal point in the field of error-correcting codes, owing to their remarkable capacity-achieving characteristics and their relevance in various modern communication systems. The basic successive cancellation (SC) approach is not optimal to use in terms of the trade-off between performance and decoding complexity. SC-Creeper algorithm performs better with about the same low complexity as the SC version of the algorithm. However, the SC-Creeper algorithm did not have the ability to use the candidate list as a measure to improve performance and refine the search for the true codeword. To compare with successive cancellation list (SCL) approach and the ability to use more computing memory, the SCL-Creeper method was developed, using two additional lists. This method can also be used as a development of Fano algorithms for polar codes (mainly, Fano decoding in polar decoding does not use lists). This paper addresses the challenge of computational complexity in polar code decoding by integrating a list structure with the SC-Creeper algorithm. Building on prior research that introduced the concept of SC-Creeper, the study focuses on enhancing error correction performance while mitigating computational burden. The first chapters describe the polar encoding process and basic decoding technologies, then discuss the basic Creeper algorithm. In the following chapters, the authors describe a modified version of the two-list Creeper approach (that is, the SCL-Creeper version of the algorithm). Extensive simulations and numerical analysis presented in the paper underscore the tangible advantages of this novel decoding strategy. Leveraging the basic list algorithm, renowned for its superior error correction capabilities, the research explores the integration of Creeper to systematically prune unnecessary decoding paths. The resulting SCL-Creeper hybrid approach aims to strike a balance between error correction efficiency and computational complexity. Finally, the optimal selection of parameters for the SCL-Creeper approach and future directions in the research of the list version of the fast Creeper algorithm are discussed.