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A Code for Positive Integers with Grouping of Message Length Using Geometric Progression
Hirofumi NAKAMURA Sadayuki MURASHIMA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2001/09/01
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Theory
positive integer code, asymptotically optimal code, length information, geometric progression,
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A positive integer code EXEb,h,d(b1, h1,d0) is proposed. Its codeword for a positive integer n consists of three kinds of information: (1) how many times the number of n's digits can be subtracted by the terms of a progression including a geometric progression, (2) the rest of the subtractions, and (3) given value of the positive integer n. EXEb,h,d is a non-recursive type code. It is an asymptotically optimal code (for d1) and preserves the lexicographic,length, and number orders (for bh+2). Some examples of EXEb,h,d are also presented. Their codeword lengths are found to be shorter than the Amemiya and Yamamoto code CEk except for small positive integers.