Manickam, SK (2019) Probability mass functions for which sources have the maximum minimum expected length. In: 25th National Conference on Communications, NCC 2019, 20 - 23 February 2019, Bangalore.
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Abstract
Let mathcal P - n be the set of all probability mass functions (PMFs) (p- 1 ,p- 2 , ldots, p- n ) that satisfy p- i > 0 for 1leq ileq n. Define the minimum expected length function mathcal L - D :mathcal P - n rightarrow mathbb R such that mathcal L - D (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 mathcal L - D attains its maximum value at the uniform distribution. Further, when n is of the form D m , with m being a positive integer, PMFs other than the uniform distribution at which mathcal L - D 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.
| Item Type: | Conference Paper |
|---|---|
| Publication: | 25th National Conference on Communications, NCC 2019 |
| Publisher: | Institute of Electrical and Electronics Engineers Inc. |
| Additional Information: | The copyright for this article belongs to the Author(s). |
| Keywords: | Functions, Expected length; Memoryless source; Positive integers; Prefix codes; Probability mass function; Source distribution; Uniform distribution, Probability distributions |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 28 Oct 2022 05:54 |
| Last Modified: | 28 Oct 2022 05:54 |
| URI: | https://eprints.iisc.ac.in/id/eprint/77726 |
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