Channel Upgradation for Non-Binary Input Alphabets and MACs

TL;DR

This paper introduces a method to approximate large-output channels with smaller-output versions, facilitating the construction of capacity-achieving polar codes for non-binary, asymmetric channels and other information-theoretic settings.

Contribution

It presents a novel channel upgrading technique applicable to non-symmetric, non-binary input channels, enhancing polar code design and related information theory applications.

Findings

Effective channel approximation for non-binary inputs

Improved polar code construction for asymmetric channels

Applications in wiretap and lossy source coding scenarios

Abstract

Consider a single-user or multiple-access channel with a large output alphabet. A method to approximate the channel by an upgraded version having a smaller output alphabet is presented and analyzed. The original channel is not necessarily symmetric and does not necessarily have a binary input alphabet. Also, the input distribution is not necessarily uniform. The approximation method is instrumental when constructing capacity achieving polar codes for an asymmetric channel with a non-binary input alphabet. Other settings in which the method is instrumental are the wiretap setting as well as the lossy source coding setting.