Motivated by communication systems with constrained complexity, we consider the problem of input symbol selection for discrete memoryless channels (DMCs). Given a DMC, the goal is to find a subset of its input alphabet, so that the optimal input distribution that is only supported on these symbols maximizes the capacity among all other subsets of the same size (or smaller). We observe that the resulting optimization problem is non-concave and non-submodular, and so generic methods for such cases do not have theoretical guarantees. We derive an analytical upper bound on the capacity loss when selecting a subset of input symbols based only on the properties of the transition matrix of the channel. We propose a selection algorithm that is based on input-symbols clustering, and an appropriate choice of representatives for each cluster, which uses the theoretical bound as a surrogate objective function. We provide numerical experiments to support the findings.

翻译：受复杂度受限的通信系统启发，我们研究了离散无记忆信道（DMC）的输入符号选择问题。给定一个DMC，目标是从其输入字母表中找到一个子集，使得仅在这些符号上支持的最优输入分布能够在所有相同规模（或更小）的子集中实现容量最大化。我们观察到由此产生的优化问题既非凹函数也非子模函数，因此针对此类情况的通用方法缺乏理论保证。我们推导了仅基于信道转移矩阵特性选择输入符号子集时容量损失的解析上界。提出了一种基于输入符号聚类及为每个聚类选择适当代表元的选取算法，该算法以理论界作为代理目标函数。我们通过数值实验验证了研究结果。