This question is non-trivial even for s=0. Here it becomes: let Alice choose a probability p (which has to be on the form p=k2n but this is irrelevant for large n) and Bob observes the binomially distributed number B(m,p). With which distribution should Alice choose p to maximize the capacity of this channel.
This question is non-trivial even for s=0. Here it becomes: let Alice choose a probability p (which has to be on the form p=k2n but this is irrelevant for large n) and Bob observes the binomially distributed number B(m,p). With which distribution should Alice choose p to maximize the capacity of this channel.