TY - JOUR
T1 - Properties of a word-valued source with a non-prefix-free word set
AU - Ishida, Takashi
AU - Goto, Masayuki
AU - Matsushima, Toshiyasu
AU - Hirasawa, Shigeichi
PY - 2006/12
Y1 - 2006/12
N2 - Recently, a word-valued source has been proposed as a new class of information source models. A word-valued source is regarded as a source with a probability distribution over a word set. Although a word-valued source is a nonstationary source in general, it has been proved that an entropy rate of the source exists and the Asymptotic Equipartition Property (AEP) holds when the word set of the source is prefix-free. However, when the word set is not prefix-free (non-prefix-free), only an upper bound on the entropy density rate for an i.i.d. word-valued source has been derived so far. In this paper, we newly derive a lower bound on the entropy density rate for an i.i.d. word-valued source with a finite non-prefix-free word set. Then some numerical examples are given in order to investigate the behavior of the bounds.
AB - Recently, a word-valued source has been proposed as a new class of information source models. A word-valued source is regarded as a source with a probability distribution over a word set. Although a word-valued source is a nonstationary source in general, it has been proved that an entropy rate of the source exists and the Asymptotic Equipartition Property (AEP) holds when the word set of the source is prefix-free. However, when the word set is not prefix-free (non-prefix-free), only an upper bound on the entropy density rate for an i.i.d. word-valued source has been derived so far. In this paper, we newly derive a lower bound on the entropy density rate for an i.i.d. word-valued source with a finite non-prefix-free word set. Then some numerical examples are given in order to investigate the behavior of the bounds.
KW - Asymptotic Equipartition Property (AEP)
KW - Entropy density rate
KW - Entropy rate
KW - Non-prefix-free
KW - Word set
KW - Word-valued source
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U2 - 10.1093/ietfec/e89-a.12.3710
DO - 10.1093/ietfec/e89-a.12.3710
M3 - Article
AN - SCOPUS:33845565335
SN - 0916-8508
VL - E89-A
SP - 3710
EP - 3723
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IS - 12
ER -