I have a Binary Erasure channel. The channel matrix is given as follows: P(Y=0|X=0) = p, P(Y=0|X=1) = 1-p, P(Y=1|X=0) = 1-p, P(Y=1|X=1) = p. Is there any "analytical" way to find possible distributions P' such that $||P - P'||_1 \leq \delta$?
I was hoping to find any analytical solution. Is it possible to find all such distances? There maybe a possible linear program formulation of this problem, but I am more interested in the analytical approach.