TY - GEN

T1 - Asymptotics of the entropy rate for a hidden Markov process

AU - Zuk, Or

AU - Kanter, I.

AU - Domany, Eytan

N1 - Place of conference:USA

PY - 2005

Y1 - 2005

N2 - 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/.

AB - 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/.

UR - https://scholar.google.co.il/scholar?q=Asymptotics+of+the+Entropy+Rate+for+a+Hidden+MarkovProcess&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - Data Compression Conference, 2005. Proceedings. DCC 2005

PB - IEEE

ER -