Differential properties of polar codes

Abstract

This paper discusses the features of polar coding as a differential encoder for a binary erasure channel. One of the modern methods of error-correcting coding is polar codes, which has great prospects in the development of current and future wireless communication systems. At the moment, polar coding is used only in fifth-generation systems. In this paper, a description of polar coding is presented, a description of a polar decoding algorithm capable of restoring messages with an error probability close to 1 is presented, and a general model of a binary channel with erasures is described. The channel model represents a fixed number of introduced errors, depending on the size of the transmitted message. The result of the study is the dependence of the bit-error ratio (BER) on the error probability for low, medium and high code rates, which illustrate the possibility of the polar coding algorithm to restore a message with a partially or completely inverse data stream.

Keywords

• polar codes
• block codes
• differential encoder
• generator matrix