  Motivated by a greedy approach for generating {\it{information stable}}
processes, we prove a universal maximum likelihood (ML) upper bound on the
capacities of discrete information stable channels, including the binary
erasure channel (BEC), the binary symmetric channel (BSC) and the binary
deletion channel (BDC). The bound is derived leveraging a system of equations
obtained via the Karush-Kuhn-Tucker conditions. Intriguingly, for some
memoryless channels, e.g., the BEC and BSC, the resulting upper bounds are
tight and equal to their capacities. For the BDC, the universal upper bound is
related 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-$n$ binary
sequence. To get explicit upper bounds from the universal upper bound, it
requires to compute a maximization of the matching functions over a Hamming
cube containing all length-$n$ binary sequences. Calculating the maximization
exactly is hard. Instead, we provide a combinatorial formula approximating it.
Under certain assumptions, several approximations and an {\it{explicit}} upper
bound for deletion probability $d\geq 1/2$ are derived.
