We study the problem of maximizing R{é}nyi entropy of order $2$ (equivalently, minimizing the index of coincidence) over the set of joint distributions with prescribed marginals. A closed-form optimizer is known under a feasibility condition on the marginals; we show that this condition is highly restrictive. We then provide an explicit construction of an optimal coupling for arbitrary marginals. Our approach characterizes the optimizer's structure and yields an iterative algorithm that terminates in finite time, returning an exact solution after at most $p-1$ updates, where $p$ is the number of rows.

翻译：我们研究了在具有指定边际分布的联合分布集合上最大化二阶Rényi熵（等价于最小化重合指数）的问题。已知在边际分布满足可行性条件下存在闭式最优解；我们证明该条件具有高度限制性。随后，我们针对任意边际分布给出了最优耦合的显式构造方法。我们的方法通过刻画最优解的结构，提出了一种有限步终止的迭代算法，该算法最多经过$p-1$次更新即可返回精确解，其中$p$表示行数。