It is of central interest in information theory to determine whether a given vector in the entropy space is an almost entropic vector. This problem can be answered if all the information inequalities are known, but this is an extremely challenging problem. On the other hand, we can establish that a given vector is an entropy vector if we can show the existence of distribution such that the corresponding entropy vector is the same as the given vector. However, there is no known algorithm to solve this problem. Only for the simplest case of binary entropy vectors, an algorithm is known to solve this problem. In this paper, we present a recursive algorithm to determine whether a given vector is a quasi-uniform entropy vector and, if it is, to return a consistent quasi-uniform distribution. We also present two applications of the recursive procedure: (i) to generate all quasi-uniform distributions motivated by the problem of finding the smallest quasi-uniform distribution such that its entropy vector violates the well known Ingleton inequality and (ii) to obtain an entropy vector (not necessarily quasi-uniform) near to a target vector in the entropy space for random variables with given alphabet size.

中文翻译：

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验证准均匀熵向量的递归算法及其应用


确定熵空间中的给定向量是否是几乎熵向量是信息论的核心兴趣。如果所有的信息不等式都已知，这个问题就可以得到解答，但这是一个极具挑战性的问题。另一方面，如果我们可以证明分布的存在性使得相应的熵向量与给定向量相同，则可以确定给定向量是熵向量。然而，没有已知的算法可以解决这个问题。仅对于二元熵向量的最简单情况，已知有一种算法可以解决该问题。在本文中，我们提出了一种递归算法来确定给定向量是否是准均匀熵向量，如果是，则返回一致的准均匀分布。我们还提出了递归过程的两个应用：（i）生成所有准均匀分布，其动机是找到最小的准均匀分布，使其熵向量违反众所周知的英格尔顿不等式；（ii）获得对于给定字母大小的随机变量，熵向量（不一定是准均匀的）接近熵空间中的目标向量。