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

翻译：构造最优AIFV码的问题可视为构造最小成本马尔可夫链的一个特例。本文首次完整证明了已知迭代算法在构造此类马尔可夫链时的正确性。近期研究表明，通过先构建马尔可夫链多面体，再对其执行椭球算法求解线性规划，可高效解决马尔可夫链问题。本文的第二个成果在于：针对AIFV情形，该多面体的特殊性质允许改用简单的二分搜索求解相应的线性规划问题。