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.

In this paper, we propose a novel multiple access rateless network coding scheme for machine-to-machine (M 2M) communications. The presented scheme is capable of increasing transmission efficiency by reducing occupied time slots yet with high decoding success rates. Unlike existing state-of-the-art distributed rateless coding schemes, the proposed rateless network coding can dynamically recode by using simple yet effective XOR operations, which is suitable for M2M erasure networks. Simulation results and analysis demonstrate that the proposed scheme outperforms the existing distributed rateless network coding schemes in the scenario of M2M multicast network with heterogeneous erasure features.