Asymptotic Optimality of Antidictionary Codes

TL;DR

This paper proves the asymptotic optimality of antidictionary codes for stationary ergodic Markov sources with arbitrary transition probabilities, extending previous results limited to balanced binary sources.

Contribution

It establishes the asymptotic optimality of static and dynamic antidictionary codes for a broader class of Markov sources beyond the balanced binary case.

Findings

Proves optimality for stationary ergodic Markov sources with transition probability p.

Extends previous results from balanced binary sources to general Markov sources.

Validates the effectiveness of antidictionary codes in more general settings.

Abstract

An antidictionary code is a lossless compression algorithm using an antidictionary which is a set of minimal words that do not occur as substrings in an input string. The code was proposed by Crochemore et al. in 2000, and its asymptotic optimality has been proved with respect to only a specific information source, called balanced binary source that is a binary Markov source in which a state transition occurs with probability 1/2 or 1. In this paper, we prove the optimality of both static and dynamic antidictionary codes with respect to a stationary ergodic Markov source on finite alphabet such that a state transition occurs with probability $p (0 < p \leq 1)$.