We consider finite-state channels (FSCs) where the channel state is stochastically dependent on the previous channel output. We refer to these as Noisy Output is the STate (NOST) channels. We derive the feedback capacity of NOST channels in two scenarios: with and without causal state information (CSI) available at the encoder. If CSI is unavailable, the feedback capacity is C FB = max P (x|y ′ ) I(X; Y |Y ′ ), while if it is available at the encoder, the feedback capacity is C FB-CSI = max P (u|y ′ ),x(u,s ′ ) I(U ; Y |Y ′ ), where U is an auxiliary RV with finite cardinality. In both formulas, the output process is a Markov process with stationary distribution. The derived formulas generalize special known instances from the literature, such as where the state is i.i.d. and where it is a deterministic function of the output. C FB and C FB-CSI are also shown to be computable via convex optimization problem formulations. Finally, we present an example of an interesting NOST channel for which CSI available at the encoder does not increase the feedback capacity.
We consider finite-state channels (FSCs) where the channel state is stochastically dependent on the previous channel output. We refer to these as Noisy Output is the STate (NOST) channels. We derive the feedback capacity of NOST channels in two scenarios: with and without causal state information (CSI) available at the encoder. If CSI is unavailable, the feedback capacity iswhile if it is available at the encoder, the feedback capacity iswhere U is an auxiliary random variable with finite cardinality. In both formulas, the output process is a Markov process with stationary distribution. The derived formulas generalize special known instances from the literature, such as where the state is distributed i.i.d. and where it is a deterministic function of the output. C FB and C FB-CSI are also shown to be computable via concave optimization problem formulations. Finally, we give a sufficient condition under which CSI available at the encoder does not increase the feedback capacity, and we present an interesting example that demonstrates this.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.