Probability Mass Functions for which Sources have the Maximum Minimum Expected Length
Shivkumar K. Manickam · 2019
Let Pnbe the set of all probability mass functions (PMFs) (p1, p2, . . . , pn) that satisfy pi> 0 for 1 ≤ i ≤ n. DeIne the minimum expected length function LD: Pn→ R such that LD(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 LDattains its maximum value at the uniform distribution. Further, when n is of the form Dm, with m being a positive integer, PMFs other than the uniform distribution at which LDattains 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.