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Abstract: Noncontrollable finite-state channels FSCs are FSCs in which the channelinputs have no influence on the channel states, i.e., the channel states evolvefreely. Since single-letter formulae for the channel capacities are rarelyavailable for general noncontrollable FSCs, computable bounds are usuallyutilized to numerically bound the capacities. In this paper, we take thedelayed channel state as part of the channel input and then define the {\emdirected information rate} from the new channel input including the source andthe delayed channel state sequence to the channel output sequence. With thistechnique, we derive a series of upper bounds on the capacities ofnoncontrollable FSCs with-without feedback. These upper bounds can be achievedby conditional Markov sources and computed by solving an average reward perstage stochastic control problem ARSCP with a compact state space and acompact action space. By showing that the ARSCP has a uniformly continuousreward function, we transform the original ARSCP into a finite-state andfinite-action ARSCP that can be solved by a value iteration method. Under amild assumption, the value iteration algorithm is convergent and delivers anear-optimal stationary policy and a numerical upper bound.



Autor: Xiujie Huang, Aleksandar Kavcic, Xiao Ma

Fuente: https://arxiv.org/



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