On the Construction of Prefix-Free and Fix-Free Codes with Specified Codeword Compositions

TL;DR

This paper develops algorithms for constructing prefix-free and fix-free codes with specified compositions, including polynomial-time methods for certain classes and approximation algorithms for near-optimal solutions under general costs.

Contribution

It introduces a polynomial-time algorithm for fix-free code construction with specified compositions for distinct codes and an approximation algorithm for near-optimal fix-free codes with general costs.

Findings

Polynomial-time algorithm for fix-free codes with specified compositions

Approximation algorithm for near-optimal fix-free codes with general costs

Effective construction methods for specific classes of codes

Abstract

We investigate the construction of prefix-free and fix-free codes with specified codeword compositions. We present a polynomial time algorithm which constructs a fix-free code with the same codeword compositions as a given code for a special class of codes called distinct codes. We consider the construction of optimal fix-free codes which minimizes the average codeword cost for general letter costs with uniform distribution of the codewords and present an approximation algorithm to find a near optimal fix-free code with a given constant cost.