Shortened Polarization-Adjusted Convolutional (PAC) Codes and List Decoding

Abstract: Shortening is a standard rate-matching method for polar codes in wireless communications. Since the block length of polarization-adjusted convolutional (PAC) codes is also limited to the integer powers of two, they also require rate-matching. We analyze the limitations of existing shortening patterns for PAC codes and explore their feasibility. A novel shortening scheme for PAC codes is then proposed based on list decoding, where the receiver is allowed to treat the values of the deleted bits as undetermined. This scheme uses a specialized PAC codeword and activates multiple decoding paths during the initialization of list decoding, enabling it to achieve the desired reliability.

Keywords: polarization-adjusted convolutional codes; rate-matching; shortened codes; list decoding