Probability Mass Functions for which Sources have the Maximum Minimum Expected Length

Let P be the set of all probability mass functions (PMFs),p) that satisfy p, > 0 for 1 < z < n. Define the minimum expected length function fp Pr, R such that CD (P) is the minimum expected length of a prefix code, formed out of an alphabet of size D, for the discrete memoryless source having P as its source distribution. It is well-known that the function CD attains its maximum value at the uniform distribution. Further, when n is of the form TY', with m being a positive integer, PMFs other than the uniform distribution at which CD attains its maximum value are known. However, a complete characterization of all such PMFs at which the minimum expected length function attains its maximum value has not been done so far. This is done in this paper.