Improved Hybrid Design of Polar Codes and Multi-Kernel Polar Codes

In this paper we propose a novel frozen set design for polar codes and multi-kernel polar codes. We improve the existing hybrid distance-reliability design by minimizing the upper bound of the overall system error probability instead of minimizing its lower bound as previously proposed. This allows to better trade reliabilities of the input bits against distance properties of the code. We describe the new design approach, propose a greedy algorithm to limit the complexity of the code construction process, and evaluate its performance through numerical examples. In both MK polar codes and conventional polar codes, a substantial performance improvement is observed, matching the performance of CRC-aided polar codes under SCL without the need for a CRC.