Fast List Decoders for Polarization-Adjusted Convolutional (PAC) Codes

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 latency. In this paper, to improve the speed of list decoding, fast list decoders for PAC codes are proposed. We define four types of constituent nodes and provide fast list decoding algorithms 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 latency with negligible performance degradation.