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Motivated by a greedy approach for generating {\it{information stable}}processes, we prove a universal maximum likelihood (ML) upper bound on thecapacities of discrete information stable channels, including the binaryerasure channel (BEC), the binary symmetric channel (BSC) and the binarydeletion channel (BDC). The bound is derived leveraging a system of equationsobtained via the Karush-Kuhn-Tucker conditions. Intriguingly, for somememoryless channels, e.g., the BEC and BSC, the resulting upper bounds aretight and equal to their capacities. For the BDC, the universal upper bound isrelated to a function counting the number of possible ways that a length-$\lo$binary subsequence can be obtained by deleting $n-m$ bits (with $n-m$ close to$nd$ and $d$ denotes the {\it{deletion probability}}) of a length-$n$ binarysequence. To get explicit upper bounds from the universal upper bound, itrequires to compute a maximization of the matching functions over a Hammingcube containing all length-$n$ binary sequences. Calculating the maximizationexactly is hard. Instead, we provide a combinatorial formula approximating it.Under certain assumptions, several approximations and an {\it{explicit}} upperbound for deletion probability $d\geq 1/2$ are derived.

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