On the Capacity of the One-Bit Deletion and Duplication Channel

TL;DR

This paper derives the capacity of a one-bit deletion and duplication channel in the regime where error probabilities are small, providing insights into the limits of reliable communication under such errors.

Contribution

It provides the first asymptotic capacity expression for the one-bit deletion and duplication channel and extends it to segmented channels with multiple blocks.

Findings

Capacity expression in the asymptotic regime

Asymptotic capacity for segmented channels

Insights into reliable communication limits

Abstract

The one-bit deletion and duplication channel is investigated. An input to this channel consists of a block of bits which experiences either a deletion, or a duplication, or remains unchanged. For this channel a capacity expression is obtained in a certain asymptotic regime where the deletion and duplication probabilities tend to zero. As a corollary, we obtain an asymptotic expression for the capacity of the segmented deletion and duplication channel where the input now consists of several blocks and each block independently experiences either a deletion, or a duplication, or remains unchanged.