Structural Extension of Polar Codes via Simplex Kernels

In this paper, we introduce a structural extension method of polar codes as a new code modification method. Structural extension is a systematic method of generating additional codeword bits from the mother code by selecting intermediate bits obtained in the middle of the polar encoding. We start by studying simplex-extension from a 2× 2 local polarization kernel, and then, we generalize this method to construct polar codes of arbitrary lengths. This extension method does not change the original polar code structure, and thus, the conventional encoder and decoder can be employed with a slight modification. We present a code construction tool by modifying density evolution to design punctured, shortened, and extended polar codes. By analysis and numerical experiments, we show that the proposed structural extension method enables to achieve an excellent tradeoff between performance and implementation complexity.