Computer Science – Information Theory
Scientific paper
2009-04-07
Computer Science
Information Theory
24 pages, One column, 6 figures; submitted to IEEE Transaction on Information Theory
Scientific paper
Noncontrollable finite-state channels (FSCs), also known as Markov channels without intersymbol interference (ISI), are finite-state channels in which the channel inputs have no influence on the channel states, i.e., the channel states evolve freely. Since single-letter formulae of the channel capacities are rarely available for general noncontrollable FSCs, computable bounds are usually utilized to evaluate numerically the capacities from above and below. In this paper, we take the delayed channel state as part of the channel input and then mathematically define the {\em directed information rate} from the new channel input (including the source and the delayed channel state) sequence to the channel output sequence. With this technique, we derive a series of upper bounds on the capacities of noncontrollable FSCs with/without feedback. It is shown that these upper bounds can be achieved by conditional Markov sources and computed by solving an average reward per stage stochastic control problem (ARSCP) with a compact state space and a compact policy space. By showing that the ARSCP has a uniformly continuous reward function, we transform the original ARSCP into a finite-state and finite-policy ARSCP that can be solved by a value iteration method. Under a mild assumption, the value iteration algorithm is convergent and delivers a near-optimal stationary policy as well as a numerical upper bound.
Huang Xiujie
Kavcic Aleksandar
Ma Xiao
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