Better Algorithms for Constructing Minimum Cost Markov Chains and AIFV Codes

TL;DR

This paper improves algorithms for constructing optimal AIFV codes by proving correctness of an iterative method and introducing a simpler linear programming approach specific to the AIFV case.

Contribution

It provides the first complete proof of correctness for an iterative algorithm and simplifies the linear programming solution for AIFV code construction.

Findings

Proved correctness of the iterative algorithm for Markov chain construction.

Developed a binary search method for solving the linear program in AIFV codes.

Enhanced efficiency in constructing optimal AIFV codes.

Abstract

The problem of constructing optimal AIFV codes is a special case of that of constructing minimum cost Markov Chains. This paper provides the first complete proof of correctness for the previously known iterative algorithm for constructing such Markov chains. A recent work describes how to efficiently solve the Markov Chain problem by first constructing a Markov Chain Polytope and then running the Ellipsoid algorithm for linear programming on it. This paper's second result is that, in the AIFV case, a special property of the polytope instead permits solving the corresponding linear program using simple binary search