A Code Whose Codeword Length is Shorter than n in Almost All of Sufficiently Large Positive Integers

Hirofumi NAKAMURA  Sadayuki MURASHIMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.4   pp.1132-1139
Publication Date: 2006/04/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.4.1132
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Theory
recursive-type positive integer code,  length information,  log-star function,  asymptotically optimal code,  universality,  

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A recursive-type positive integer code is proposed. It prefixes the information about the length of the component of the codeword recursively. It is an asymptotically optimal code. The codeword length for a positive integer n is shorter than n bits in almost all of sufficiently large positive integers, where n is the log-star function.