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Relationship among Complexities of Individual Sequences over Countable Alphabet
Shigeaki KUZUOKA Tomohiko UYEMATSU
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2006/07/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
empirical entropy, individual sequence, Lempel-Ziv algorithm, universal source coding,
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This paper investigates some relations among four complexities of sequence over countably infinite alphabet, and shows that two kinds of empirical entropies and the self-entropy rate regarding a Markov source are asymptotically equal and lower bounded by the maximum number of phrases in distinct parsing of the sequence. Some connections with source coding theorems are also investigated.