Novel Bounds on the Capacity of the Binary Deletion Channel

TL;DR

This paper introduces new upper and lower bounds on the capacity of the binary deletion channel, improving existing bounds and narrowing the gap between known limits, especially for low deletion probabilities.

Contribution

The paper develops four novel upper bounds using genie-aided information and introduces inequalities for more tractable results, advancing understanding of the channel capacity.

Findings

Most bounds improve existing ones for various deletion probabilities.

New bounds significantly narrow the gap between upper and lower capacity limits.

Simple lower bounds are nearly as effective as the best known for low deletion probabilities.

Abstract

We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined random processes. Since some of the proposed bounds involve infinite series, we also introduce provable inequalities that lead to more manageable results. For most values of the deletion probability, these bounds improve the existing ones and significantly narrow the gap with the available lower bounds. Exploiting the same auxiliary processes, we also derive, as a by-product, a couple of very simple lower bounds on the channel capacity, which, for low values of the deletion probability, are almost as good as the best existing lower bounds.