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Rate Matching for Polar Codes Based on Binary Domination

By Min Jang, Seok-Ki Ahn, Hongsil Jeong, Kyung-Joong Kim, Seho Myung, Sang-Hyo Kim and Kyeongcheol Yang

Abstract

In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination. For punctured and shortened polar codes, we prove that the partial order by binary domination completely determines both incapable bit patterns (by puncturing) and fixed bit patterns (by shortening). In particular, we give a necessary and sufficient condition for an encoder output bit to be fixed by additionally shortening a single encoder input bit, as well as a necessary and sufficient condition for an encoder input bit to be made incapable by additionally puncturing a single encoder output bit. We also identify all the puncturing bit patterns yielding a given incapable bit pattern. These results provide a guidance to design a practical rate-matching scheme for polar codes. As an example, we present a rate-matching scheme based on our analytical observations. Numerical results show that it performs well over a wide range of code lengths and rates, compared with conventional rate-matching schemes.1

Topics: CONSTRUCTION, POLARIZATION, SCHEME, Polar codes, code modification, rate matching, binary domination, puncturing, shortening
Publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Year: 2019
OAI identifier: oai:oasis.postech.ac.kr:2014.oak/101525
Provided by: 포항공과대학교
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