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Probability mass functions for which sources have the maximum minimum expected length

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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Official URL: https://doi.org/10.1109/NCC.2019.8732264

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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