Derivatives of Entropy Rate in Special Families of Hidden Markov Chains
Guangyue Han, Brian Marcus
Abstract
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.
Create a lesson
Related papers
Deterministic Identification over Additive Gaussian Channels
Jonathan E. W. Huffmann, Holger Boche
Knowledge Distillation Driven Semantic NOMA with GAN Refinement for 6G Robotic Vehicle Networks
Qifei Wang, Zhen Gao, Li Qiao et al.
Real-Time Reconstruction of Markov Sources over MPR Channels
Pansee S. Elessawy, Nikolaos Pappas
Minimum Rate For Partially Observable Linear System with Side Information: LQG Plant and Gaussian-Markov Source
Sijie Li, Hyeji Kim
Spectral Approximation and Ergodic-Capacity Convergence of HMIMO Channels under Spatial-Wavenumber Domain Mismatch
Hangsong Yan, Hong Yang, Shu Sun
Sharp Minimax Regret for Infinite-Memory Logistic Prediction
Vaneet Aggarwal