Shortened PAC Codes and List Decoding

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