Conditions for Robustness of Polar Codes in the Presence of Channel Mismatch

TL;DR

This paper investigates the robustness of polar codes against channel parameter variations by framing it as a mismatch decoding problem and establishing conditions for reliable communication despite channel mismatch.

Contribution

It introduces conditions ensuring polar code robustness under channel mismatch, connecting robust design to mismatch decoding theory, especially for binary symmetric channels.

Findings

Polar codes are robust over the class of binary symmetric channels.

Conditions for reliable communication under channel mismatch are established.

The original polar code construction method is shown to be robust against parameter variations.

Abstract

A challenging problem related to the design of polar codes is "robustness against channel parameter variations" as stated in Ar{\i}kan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as a mismatch decoding problem. We propose conditions which ensure a polar encoder/decoder designed for a mismatched B-DMC can be used to communicate reliably. In particular, the analysis shows that the original polar code construction method is robust over the class of binary symmetric channels.