In the Shannon Lecture at the 2019 International Symposium on Information Theory (ISIT), Professor Arikan proposed a new coding scheme called polarization-adjusted convolutional (PAC) codes. These codes exhibit excellent error-correction performance for short-to-medium block lengths. Currently, the mainstream decoding algorithms for PAC codes mainly include sequential decoding and list decoding. Fano decoding, a type of sequential decoding, offers good error-correction performance; however, its time complexity is relatively high due to the presence of extensive backtracking processes. In this paper, a fast Fano decoding algorithm based on backtracking optimization mechanism for PAC codes is proposed. The improved algorithm we put forward mitigate the time complexity of the decoding process from two aspects: path backtracking and threshold updating strategy. It enhances the error-correcting performance of the Fano decoding algorithm by introducing the first error node metric and the second error node metric. With the efforts in the above aspects, our decoding algorithm achieves good performance in both complexity and error-correction capability.
In the Shannon Lecture at the 2019 International Symposium on Information Theory (ISIT), Professor Arikan proposed a new coding scheme called polarization-adjusted convolutional (PAC) codes. These codes exhibit excellent error-correction performance for short-to-medium block lengths. Currently, the mainstream decoding algorithms for PAC codes mainly include sequential decoding and list decoding. Fano decoding, a type of sequential decoding, offers good error-correction performance; however, its time complexity is relatively high due to the presence of extensive backtracking processes. In this paper, a fast Fano decoding algorithm based on backtracking optimization mechanism for PAC codes is proposed. The improved algorithm we put forward mitigate the time complexity of the decoding process from two aspects: path backtracking and threshold updating strategy. It enhances the error-correcting performance of the Fano decoding algorithm by introducing the first error node metric and the second error node metric. With the efforts in the above aspects, our decoding algorithm achieves good performance in both complexity and error-correction capability.
Polarization-adjusted convolutional (PAC) codes are modified polar codes in which a one-to-one convolutional transformation is employed before the classical polar transform. Fano decoding of PAC codes in the Shannon lecture at ISIT2019 showed an outstanding performance at the cost of a high time-complexity, particularly at low SNR regimes. In order to reduce this complexity, an adaptive heuristic metric is proposed that improves the comparability of the variable-length paths and adjusts itself in response to the channel noise level. This metric can significantly reduce the number of nodes visited on average in tree-traversal. Additionally, a partial rewinding of the successive cancellation process is proposed to efficiently compute the intermediate LLRs and partial sums when backtracking occurs in the Fano algorithm. This method avoids storing the intermediate results of the decoding process or restarting (full rewinding) the decoding process.
Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node withN0leaf nodes in its corresponding subtree, conventional stack decoding must either explore all 2N0paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that removes candidate paths with small path metrics while ensuring that the probability of pruning the correct path decays exponentially with the threshold. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC(128, 64) code, our method achieves up to a 70% reduction in the average number of paths without degrading error-correction performance.
Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node with N0 leaf nodes in its corresponding subtree, conventional stack decoding must either explore all 2N0 paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that removes candidate paths with small path metrics while ensuring that the probability of pruning the correct path decays exponentially with the threshold. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC(128,64) code, our method achieves up to a 70\% reduction in the average number of paths without degrading error-correction performance.
Polarization-adjusted convolutional (PAC) codes are special concatenated codes that utilize a one-to-one convolutional transform as a pre-coding step before the polar transform, thereby approaching the dispersion approximation for code (128, 64). However, current list decoders require an overly large list size to achieve near-bound performance, leading to unsatisfactory decoding latency. In this letter, we propose a fast list decoding algorithm with new special nodes for PAC codes, which effectively decreases decoding latency while preserving error-correction performance. Compared to the state-of-the-art work, the proposed algorithm can reduce decoding latency by up to 25.81% for the PAC code of length 128 with a code rate of 1/6.
A latest coding scheme named polarization-adjusted convolutional (PAC) codes is shown to provide dramatic improvement in performance as compared to polar codes under list decoding. However, to achieve this performance gain, the list size needs to be excessively large, which may cause insufferable latency. For PAC codes, utilizing special nodes can reduce the time complexity. In this letter, we propose an extension of the sequence repetition (SR) nodes to PAC codes to further reduce the decoding latency. First, we define the notion of convolution-effected repetition sequences, which helps us to decode a specific SR node. Then, we propose a fast list decoding algorithm by taking the SR nodes into consideration. Simulation results indicate that the performance of the proposed decoding algorithm is almost identical to the original list decoding algorithm while achieving a higher degree of parallelism. In particular, for a PAC code of length 128 with code rate 1/4, the decoding latency can be reduced by over 35% as compared to the state-of-the-art fast list decoder.
Abstract A latest coding scheme named polarization‐adjusted convolutional (PAC) codes is shown to approach the dispersion bound for the code (128,64) under list decoding. However, to achieve the near‐bound performance, the list size of list decoding needs to be excessively large, which leads to insufferable time complexity. In this paper, to improve the speed of list decoding, fast list decoders for PAC codes are proposed. Four types of constituent nodes are defined and fast list decoding algorithms are provided for each of them. Simulation results present that fast list decoding with three types of constituent nodes can yield exactly the same error‐correction performance as list decoding, and reduce more than 50% time steps for the code (128,64). Moreover, fast list decoding with four types of constituent nodes can further reduce decoding complexity with negligible performance degradation.