To Feed or Not to Feed Back

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 N 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 probability of initial state is positive for all states. Further, for stationary indecomposable cha...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Himanshu Asnani, Haim H. Permuter, Tsachy Weissman
• Keywords: CORR 2010, Decoder, Decoder Actions, Education, Encoder