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.
All Science Journal Classification (ASJC) codes
- Signal Processing
- Electrical and Electronic Engineering
- Applied Mathematics
- Hidden markov process (HMP)
- Taylor series