Alternating Markov Chains for Distribution Estimation in the Presence of Errors

TL;DR

This paper introduces a novel approach using alternating Markov chains to estimate distributions over noisy repetition channels, demonstrating sub-linear redundancy growth and providing a new estimation method for such noisy environments.

Contribution

It proposes a new class of distribution estimators based on alternating Markov chains tailored for noisy repetition channels, with theoretical analysis of redundancy.

Findings

Redundancy of alternating Markov chains scales sub-linearly with sequence length.

The proposed estimators effectively handle distribution estimation over noisy repetition channels.

The method offers improved efficiency in small-sample scenarios under channel noise.

Abstract

We consider a class of small-sample distribution estimators over noisy channels. Our estimators are designed for repetition channels, and rely on properties of the runs of the observed sequences. These runs are modeled via a special type of Markov chains, termed alternating Markov chains. We show that alternating chains have redundancy that scales sub-linearly with the lengths of the sequences, and describe how to use a distribution estimator for alternating chains for the purpose of distribution estimation over repetition channels.