A maximization problem related to Huffman codes

Shivkumar, KM and Kashyap, Navin (2017) A maximization problem related to Huffman codes. In: 23rd National Conference on Communications, NCC 2017, 02-04 March 2017, Chennai, India, pp. 1-6.

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Abstract

Let L = (l0, l1,⋯, ln-1) be a finite sequence of positive integers with Kraft sum (Σi 2-li) equal to 1. We call such a sequence a complete length sequence. Let Pn(L) be the set of all probability mass functions (PMFs) that have a Huffman code with codeword lengths L. For a PMF P, let L(P) denote the minimum expected length of a binary prefix-free code for P. In this paper, we show that the set L(P) : P E Pn(L) has a maximum value. A P E Pn(L) at which this maximum is attained is explicitly determined for a class of complete length sequences.

Item Type:	Conference Paper
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The Copyright of this article belongs to the Institute of Electrical and Electronics Engineers Inc.
Keywords:	Codeword length; Expected length; Finite sequence; Huffman code; Maximization problem; Positive integers; Prefix-free codes; Probability mass function; Codes (symbols)
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	09 Jun 2022 05:13
Last Modified:	09 Jun 2022 05:13
URI:	https://eprints.iisc.ac.in/id/eprint/73305

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