To Feed or Not to Feed Back
Himanshu Asnani, Haim Permuter, Tsachy Weissman

TL;DR
This paper investigates the capacity of finite state channels with controllable feedback, establishing capacity results, bounds, and algorithms for channels with action-dependent feedback and cost constraints.
Contribution
It introduces a unified framework for channels with action-controlled feedback, deriving capacity formulas, bounds, and an extension of the Blahut-Arimoto algorithm for cost-constrained actions.
Findings
Capacity characterized for channels with positive initial state probability.
Upper and lower bounds coincide for certain channels, establishing exact capacity.
Extended Blahut-Arimoto algorithm enables capacity evaluation under cost constraints.
Abstract
We study the communication over Finite State Channels (FSCs), where the encoder and the decoder can control the availability or the quality of the noise-free feedback. Specifically, the instantaneous feedback is a function of an action taken by the encoder, an action taken by the decoder, and the channel output. Encoder and decoder actions take values in finite alphabets, and may be subject to average cost constraints. We prove capacity results for such a setting by constructing a sequence of achievable rates, using a simple scheme based on 'code tree' generation, that generates channel input symbols along with encoder and decoder actions. We prove that the limit of this sequence exists. For a given block length and probability of error, we give an upper bound on the maximum achievable rate. Our upper and lower bounds coincide and hence yield the capacity for the case where the…
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