A recent result presented the expansion for the entropy rate of a hidden Markov process (HMP) as a power series in the noise variable ε. The coefficients of the expansion around the noiseless (ε = 0) limit were calculated up to 11th order, using a conjecture that relates the entropy rate of an HMP to the entropy of a process of finite length (which is calculated analytically). In this letter, we generalize and prove the conjecture and discuss its theoretical and practical consequences.
Bibliographical noteFunding Information:
Manuscript received January 4, 2006; revised January 23, 2006. The work of M. Aizenman was supported in part by the Einstein Center for Theoretical Physics and in part by the Minerva Center for Nonlinear Physics. The work of I. Kanter at the Weizmann Institute was supported by the Einstein Center for Theoretical Physics. E. Domany and O. Zuk were supported in part by the Minerva Foundation and in part by the European Community’s Human Potential Programme under Contract HPRN-CT-2002-00319, STIPCO. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Cihan Tepedelenlioglu.
- Hidden markov process (HMP)
- Taylor series