Maximum Likelihood Upper Bounds on the Capacities of Discrete Information Stable Channels

Motivated by generating information stable processes greedily, we prove a universal maximum likelihood (ML) upper bound on the capacities of discrete information stable channels. The bound is derived leveraging a system of equations obtained via the Karush-Kuhn-Tucker (KKT) conditions. Intriguingly, for some discrete memoryless channels (DMCs), for instance, the BEC and BSC, the associated upper bounds are tight and equal to their capacities. Furthermore, for discrete channels with memory, as a particular example, we apply the ML bound to the BDC. The derived upper bound is a sum-max function related to counting the number of possible ways that a length-m binary subsequence that can be obtained by deleting n-m bits (with n-m close to nd and d denotes the deletion probability) of a length-n binary sequence.