On the Capacity of Channels with Timing Synchronization Errors

TL;DR

This paper introduces a new framework for analyzing synchronization error channels, deriving bounds and exact rates for deletion and replication channels, and demonstrating convergence of approximate models to the true channel capacity.

Contribution

It presents a novel formulation for synchronization error channels, providing analytical bounds, exact capacity characterizations, and convergence results for approximate models.

Findings

Derived a tight lower bound for the binary deletion channel's symmetric information rate.

Exactly characterized the Markov-1 rate for the binary replication channel.

Showed convergence of approximate channel models to the true channel capacity as state space increases.

Abstract

We consider a new formulation of a class of synchronization error channels and derive analytical bounds and numerical estimates for the capacity of these channels. For the binary channel with only deletions, we obtain an expression for the symmetric information rate in terms of subsequence weights which reduces to a tight lower bound for small deletion probabilities. We are also able to exactly characterize the Markov-1 rate for the binary channel with only replications. For a channel that introduces deletions as well as replications of input symbols, we design approximating channels that parameterize the state space and show that the information rates of these approximate channels approach that of the deletion-replication channel as the state space grows. For the case of the channel where deletions and replications occur with the same probabilities, a stronger result in the convergence of mutual information rates is shown. The numerous advantages this new formulation presents are explored.