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Asymptotics of the entropy rate for a hidden Markov process

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3 Author(s)
Zuk, O. ; Dept. of Phys. of Complex Syst., Weizmann Inst. of Sci., Israel ; Kanter, I. ; Domany, Eytan

We calculate the Shannon entropy rate of a binary hidden Markov process (HMP), of given transition rate and noise ε (emission), as a series expansion in ε. The first two orders are calculated exactly. We then evaluate, for finite histories, simple upper-bounds of Cover and Thomas. Surprisingly, we find that for a fixed order k and history of n steps, the bounds become independent of n for large enough n. This observation is the basis of a conjecture, that the upper-bound obtained for n≥(k+3)/2 gives the exact entropy rate for any desired order k of ε.

Published in:

Data Compression Conference, 2005. Proceedings. DCC 2005

Date of Conference:

29-31 March 2005