On Matched Metric and Channel Problem
  The sufficient condition for partial function from the cartesian square of the finite set to the reals to be compatible with some metric on this set is given. It is then shown, that when afforementioned set and function are respectively a space of binary words of length n and probalities of receiving some word after sending the other word through Binary Assymetric Channel the condition is satisfied so the required metrics exist. 
Artur Poplawski
cs.IT math.IT