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 -