Efficient Implementation of the Generalized Tunstall Code Generation Algorithm

TL;DR

This paper introduces a linear-time algorithm for constructing generalized Tunstall codes, significantly improving efficiency for non-Bernoulli sources like Markov sources, with detailed complexity analysis.

Contribution

It presents a novel linear-time construction method for generalized Tunstall codes applicable to complex sources, surpassing previous algorithms in efficiency.

Findings

Achieves linear time complexity in output size

Applicable to Markov and non-Bernoulli sources

Reduces computational resources compared to prior methods

Abstract

A method is presented for constructing a Tunstall code that is linear time in the number of output items. This is an improvement on the state of the art for non-Bernoulli sources, including Markov sources, which require a (suboptimal) generalization of Tunstall's algorithm proposed by Savari and analytically examined by Tabus and Rissanen. In general, if n is the total number of output leaves across all Tunstall trees, s is the number of trees (states), and D is the number of leaves of each internal node, then this method takes O((1+(log s)/D) n) time and O(n) space.