An approach is established for maximizing the Lower bound on the Mismatch capacity (hereafter abbreviated as LM rate), a key performance bound in mismatched decoding, by optimizing the channel input probability distribution. Under a fixed channel input probability distribution, the computation of the corresponding LM rate is a convex optimization problem. When optimizing the channel input probability distribution, however, the corresponding optimization problem adopts a max-min formulation, which is generally non-convex and is intractable with standard approaches. To solve this problem, a novel dual form of the LM rate is proposed, thereby transforming the max-min formulation into an equivalent double maximization formulation. This new formulation leads to a maximization problem setup wherein each individual optimization direction is convex. Consequently, an alternating maximization algorithm is established to solve the resultant maximization problem setup. Each step of the algorithm only involves a closed-form iteration, which is efficiently implemented with standard optimization procedures. Numerical experiments show the proposed approach for optimizing the LM rate leads to noticeable rate gains.

翻译：本文提出了一种通过优化信道输入概率分布来最大化非匹配容量下界（以下简称LM率）的方法，该下界是非匹配解码中的一个关键性能界。在固定信道输入概率分布的条件下，计算相应的LM率是一个凸优化问题。然而，在优化信道输入概率分布时，相应的优化问题采用了max-min形式，该形式通常是非凸的，且难以用标准方法求解。为解决此问题，本文提出了LM率的一种新颖对偶形式，从而将max-min形式转化为等效的双重最大化形式。这一新形式导出了一个最大化问题框架，其中每个单独的优化方向都是凸的。因此，本文建立了一种交替最大化算法来求解所得的最大化问题框架。该算法的每一步仅涉及闭式迭代，可通过标准优化过程高效实现。数值实验表明，所提出的优化LM率方法带来了显著的速率增益。