Finite State Channels with Time-Invariant Deterministic Feedback

2006/08/17 by Haim H. Permuter, Permuter, Haim, Tsachy Weissman +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Cellular Automata and Applications #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques

paper · pdf · doi:10.48550/arxiv.cs/0608070

openalex publication_date 2006/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider capacity of discrete-time channels with feedback for the general case where the feedback is a time-invariant deterministic function of the output samples. Under the assumption that the channel states take values in a finite alphabet, we find an achievable rate and an upper bound on the capacity. We further show that when the channel is indecomposable, and has no intersymbol interference (ISI), its capacity is given by the limit of the maximum of the (normalized) directed information between the input X^N and the output Y^N, i.e. C = lim_{N → ∞} (1)/(N) max I(X^N → Y^N), where the maximization is taken over the causal conditioning probability Q(x^N||z^N-1) defined in this paper. The capacity result is used to show that the source-channel separation theorem holds for time-invariant determinist feedback. We also show that if the state of the channel is known both at the encoder and the decoder then feedback does not increase capacity.

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