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：本文建立了一种通过优化信道输入概率分布来最大化失配容量下界（以下简称LM速率）的方法，LM速率是失配译码中关键的性能界。在固定信道输入概率分布下，计算相应LM速率是一个凸优化问题。然而，当优化信道输入概率分布时，相应的优化问题采用极大-极小形式，通常是非凸的，且无法用标准方法求解。为解决该问题，本文提出了LM速率的一种新对偶形式，从而将极大-极小形式转化为等价的双最大化形式。这种新形式导致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，建立了一种交替最大化算法来求解由此产生的最大化问题框架。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速率的方法可带来显著的速率增益。