A note on some inequalities used in channel polarization and polar coding

TL;DR

This paper provides a unified analysis of key inequalities essential for proving channel polarization theorems in binary-input discrete memoryless channels, aiding in the understanding and development of polar coding.

Contribution

It introduces a unified approach to inequalities used in channel polarization proofs, simplifying and clarifying the theoretical foundations.

Findings

Unified treatment of inequalities in polarization proofs

Simplified proofs of channel polarization theorems

Enhanced understanding of polar coding theory

Abstract

We give a unified treatment of some inequalities that are used in the proofs of channel polarization theorems involving a binary-input discrete memoryless channel.