New Capacity Upper Bounds For Binary Deletion Channel

TL;DR

This paper introduces two new close-form upper bounds on the capacity of the binary deletion channel, improving previous bounds by up to 0.1 using Markov process-based methods.

Contribution

The paper derives two novel close-form upper bounds on the binary deletion channel capacity, enhancing existing bounds with a Markov process approach.

Findings

First bound based on auxiliary channel capacity

Second bound based on mutual information approximation

Improves previous upper bounds by up to 0.1

Abstract

This paper considers a binary channel with deletions. We derive two close form upper bound on the capacity of binary deletion channel. The first upper bound is based on computing the capacity of an auxiliary channel and we show how the capacity of auxiliary channel is the upper bound of the binary deletion channel. Our main idea for the second bound is based on computing the mutual information between the sent bits and the received bits in binary deletion channel. We approximate the exact mutual information and we give a close form expression. All bounds utilize first-order Markov process for the channel input. The second proposed upper bound improves the best upper bound [6,11] up to 0.1.