Lossless Coding with Generalised Criteria

TL;DR

This paper introduces a flexible framework for prefix codes that optimize various criteria combining maximum and average codeword lengths or redundancies, with a parametric algorithm adjusting source probabilities for bounded codeword lengths.

Contribution

It proposes a novel, unified approach to lossless coding criteria, including a parametric algorithm for source probability adjustment based on merging rules.

Findings

Framework encompasses multiple existing criteria

Algorithm effectively adjusts source probabilities

Applicable to scenarios with bounded codeword lengths

Abstract

This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the average of an exponential function of the codeword length and the average redundancy. This framework encompasses as a special case several criteria previously investigated in the literature, while relations to universal coding is discussed. The coding algorithm derived is parametric resulting in re-adjusting the initial source probabilities via a weighted probability vector according to a merging rule. The level of desirable merging has implication in applications where the maximum codeword length is bounded.