Channel capacity of polar coding with a given polar mismatched successive cancellation decoder

TL;DR

This paper investigates the achievable communication rates of polar codes when the decoder uses a mismatched channel model, defining and analyzing the 'polar mismatched capacity' with bounds and expressions.

Contribution

It introduces the concept of polar mismatched capacity, providing a theoretical framework and bounds for communication rates under mismatched decoding conditions.

Findings

Derived an expression for polar mismatched capacity

Established bounds on the achievable rates with mismatched decoding

Extended polar coding analysis to mismatched channel models

Abstract

Ar{\i}kan's polar coding, is by now a well studied technique that allows achieving the symmetric capacity of binary input memoryless channels with low complexity encoding and decoding, provided that the polar decoding architecture is used and the decoding metric is matched to the true channel. In this paper, we analyze communication rates that are achievable when the polar coding/decoding architecture is used with the decoder using an incorrect model of the channel. We define the `polar mismatched capacity' as an analogue of the classical mismatched capacity, give an expression for it, and derive bounds on it.