Polar Codes for Fast Converging Belief-Propagation Decoding

Abstract

In this work, we propose a polar code design which targets at improving convergence of belief-propagation (BP) decoding. That is, the designed polar codes can achieve a target error rate at a smaller number of iterations. In particular, we will show that reliabilities on some coded bits have stronger effects on the initial log-likelihood ratio (LLR) propagation during BP decoding. By utilizing the property, we carefully puncture and extend polar codes to speed up the convergence of BP decoding. It will be shown that polar codes based on the proposed design achieve either a target error rate at a smaller number of iterations or an improved error-rate performance at a given number of iterations as compared to existing polar codes.