On the deletion channel with small deletion probability

TL;DR

This paper develops a new method to approximate the capacity of the deletion channel with small deletion probability, showing that simple i.i.d. uniform inputs are nearly optimal in this regime.

Contribution

It introduces a series expansion approach for capacity calculation at small deletion probabilities and identifies that i.i.d. uniform inputs are nearly optimal.

Findings

Capacity can be approximated by a series expansion for small deletion probability.

The first two terms of the expansion are computed.

Optimal input distribution is i.i.d. uniform, up to the order considered.

Abstract

The deletion channel is the simplest point-to-point communication channel that models lack of synchronization. Despite significant effort, little is known about its capacity, and even less about optimal coding schemes. In this paper we intiate a new systematic approach to this problem, by demonstrating that capacity can be computed in a series expansion for small deletion probability. We compute two leading terms of this expansion, and show that capacity is achieved, up to this order, by i.i.d. uniform random distribution of the input. We think that this strategy can be useful in a number of capacity calculations.