2006/03/14 by Guangyue Han, Han, Guangyue, Brian Marcus +1
Computer Science · Mathematics · #Algorithms and Data Compression #Cellular Automata and Applications #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Dynamics and Fractals #Probability (math.PR) #cs.IT #math.IT #math.PR
paper · pdf · doi:10.48550/arxiv.cs/0603059
The relaxed condtions for entropy rate and examples are taken out (to be part of another paper). The section about general principle and an example to determine the domain of analyticity is taken out (to be part of another paper). A section about binary Markov chains corrupted by binary symmetric noise is added
openalex publication_date 2006/03/14 · arxiv created 2006/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise. Namely, they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time. We generalize this result to a natural class of hidden Markov chains called ``Black Holes.'' We also discuss in depth special cases of binary Markov chains observed in binary symmetric noise, and give an abstract formula for the first derivative in terms of a measure on the simplex due to Blackwell.