Non prefix-free codes for constrained sequences

TL;DR

This paper explores the use of non prefix-free variable length codes for efficiently encoding constrained Markov sequences, relaxing classical conditions to improve compression and computational performance.

Contribution

It introduces a relaxed inequality condition for unique decodability, enabling the use of non prefix-free codes in constrained sequence coding.

Findings

Relaxed Kraft inequality for constrained sequences

Non prefix-free codes can achieve better compression

Improved computational efficiency in coding

Abstract

In this paper we consider the use of variable length non prefix-free codes for coding constrained sequences of symbols. We suppose to have a Markov source where some state transitions are impossible, i.e. the stochastic matrix associated with the Markov chain has some null entries. We show that classic Kraft inequality is not a necessary condition, in general, for unique decodability under the above hypothesis and we propose a relaxed necessary inequality condition. This allows, in some cases, the use of non prefix-free codes that can give very good performance, both in terms of compression and computational efficiency. Some considerations are made on the relation between the proposed approach and other existing coding paradigms.