Polar Codes

Abstract

Polar code was invented by Prof. Erdal Arikan of Bilkent University in Turkey in 2008. So far, polar code is the only channel coding scheme that can reach Shannon’s limit, whereas all other coding schemes can just approach Shannon’s limit. Due to the relatively high complexity of its encoding and decoding, polar code did not get wide attention right after it was proposed. This chapter discusses how polar codes were first proposed. It uses the Bhattacharyya parameter for capacity analysis to explain the principle of polar codes. Polar code encoder is to select the suitable sub-channels for data, put frozen bits to bad sub-channels, and then perform logic operations. A polar code sequence is also called the determiner of good channels, e.g., to determine the bit indices for encoded bits before polar encoding. The systematic polar code can be considered as a special case of non-systematic polar code. It can be obtained by selecting appropriate bits as frozen bits.