Properties of the Polarization Transformations for the Likelihood Ratios of Symmetric B-DMCs

TL;DR

This paper studies how likelihood ratios evolve in symmetric B-DMCs during channel polarization, offering new insights into the process and addressing computational approximation issues.

Contribution

It introduces a novel analysis of likelihood ratio transformations in symmetric B-DMCs, enhancing understanding of channel polarization dynamics.

Findings

Provides a new perspective on likelihood ratio evolution

Addresses approximation problems in likelihood ratio computations

Enhances theoretical understanding of channel polarization

Abstract

In this paper we investigate, starting with a symmetric B-DMC, the evolution of various probabilities of the likelihood ratios of the synthetic channels created by the recursive application of the basic polarization transformations. The analysis provides a new perspective into the theory of channel polarization initiated by Ar{\i}kan and helps us to address a problem related to approximating the computations of the likelihood ratios of the synthetic channels.