On the Relationships among Optimal Symmetric Fix-Free Codes

TL;DR

This paper explores the structure and generation of optimal symmetric fix-free codes, which are palindrome-based prefix codes, revealing new methods for their construction and simplification in search processes.

Contribution

It introduces a new approach to generate all optimal symmetric fix-free codes through simple manipulations from a single code, improving understanding and search efficiency.

Findings

Number of optimal code sequences grows slowly with code size

All optimal codes can be generated from a single initial code

Simplified search process for optimal codes

Abstract

Symmetric fix-free codes are prefix condition codes in which each codeword is required to be a palindrome. Their study is motivated by the topic of joint source-channel coding. Although they have been considered by a few communities they are not well understood. In earlier work we used a collection of instances of Boolean satisfiability problems as a tool in the generation of all optimal binary symmetric fix-free codes with n codewords and observed that the number of different optimal codelength sequences grows slowly compared with the corresponding number for prefix condition codes. We demonstrate that all optimal symmetric fix-free codes can alternatively be obtained by sequences of codes generated by simple manipulations starting from one particular code. We also discuss simplifications in the process of searching for this set of codes.