On the puncturing patterns for punctured polar codes

Puncturing is widely used to generate rate-compatible codes. However, for punctured polar codes, some puncturing patterns may greatly affect the split bit channels and cause considerable performance loss. In this paper, we aim to investigate how the split bit channels are affected by various puncturing patterns, and then evaluate the performances of these patterns. We propose a search algorithm to design good punctured polar codes, and prove that designing the optimal puncturing pattern for output bits is equivalent to finding the optimal puncturing pattern for frozen bits. We also propose a heuristic approach based on the idea of polarization to select the position of each punctured output bit, and simulations show that the puncturing pattern designed this way almost achieves the same performance as the optimal one selected by exhaustive search.