Deinterleaving Finite Memory Processes via Penalized Maximum Likelihood

TL;DR

This paper introduces a penalized maximum likelihood method for deinterleaving finite-memory processes, ensuring consistent recovery of component processes without prior knowledge of their structure, even with limited data.

Contribution

It proposes a novel deinterleaving scheme based on penalized maximum likelihood that guarantees strong consistency and can recover all possible representations under certain conditions.

Findings

The scheme is strongly consistent as sequence length increases.

It can recover all representations under specific switch conditions.

Experimental results show good practical performance with short samples.

Abstract

We study the problem of deinterleaving a set of finite-memory (Markov) processes over disjoint finite alphabets, which have been randomly interleaved by a finite-memory switch. The deinterleaver has access to a sample of the resulting interleaved process, but no knowledge of the number or structure of the component Markov processes, or of the switch. We study conditions for uniqueness of the interleaved representation of a process, showing that certain switch configurations, as well as memoryless component processes, can cause ambiguities in the representation. We show that a deinterleaving scheme based on minimizing a penalized maximum-likelihood cost function is strongly consistent, in the sense of reconstructing, almost surely as the observed sequence length tends to infinity, a set of component and switch Markov processes compatible with the original interleaved process. Furthermore, under certain conditions on the structure of the switch (including the special case of a memoryless switch), we show that the scheme recovers \emph{all} possible interleaved representations of the original process. Experimental results are presented demonstrating that the proposed scheme performs well in practice, even for relatively short input samples.