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.
Polarization-adjusted convolutional (PAC) coding is a good concatenation of convolutional codes and polar codes. For short block-length codes (
N≤128), PAC codes with a sequential decoding or a list decoding with large list-sizes (
L≥128) can achieve better block-error-rate (BLER) performance than polar codes with CRC-aided list decoding. However, the PAC codes have no BLER performance advantage when the list decoding is with small list-sizes (
L≤8). In this letter, tail-biting PAC (TB-PAC) coding is proposed, in which tail-biting convolutional pre-transformation is applied. A multi-round list decoding with small list-sizes is provided for TB-PAC codes, in which an early-stopping method is designed to control the number of rounds. In each round, the tail-biting bits are assigned various initial path-values and also used as a check at the end, which helps the correct path be distinguishable. The proposed small-sizes list decoding can help the TB-PAC codes achieve much better BLER performance than the polar/PAC codes.
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.