Asymptotics of the entropy rate for a hidden Markov process

Or Zuk, I. Kanter, Eytan Domany

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We calculate the Shannon entropy rate of a binary hidden Markov process (HMP), of given transition rate and noise /spl epsiv/ (emission), as a series expansion in /spl epsiv/. 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/spl ges/(k+3)/2 gives the exact entropy rate for any desired order k of /spl epsiv/.
Original languageAmerican English
Title of host publicationData Compression Conference, 2005. Proceedings. DCC 2005
StatePublished - 2005

Bibliographical note

Place of conference:USA


Dive into the research topics of 'Asymptotics of the entropy rate for a hidden Markov process'. Together they form a unique fingerprint.

Cite this