# Finite State Channels With Time-Invariant Deterministic Feedback

@article{Permuter2009FiniteSC, title={Finite State Channels With Time-Invariant Deterministic Feedback}, author={Haim H. Permuter and Tsachy Weissman and Andrea J. Goldsmith}, journal={IEEE Transactions on Information Theory}, year={2009}, volume={55}, pages={644-662} }

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 a sequence of achievable rates and a sequence of upper bounds on the capacity. The achievable rates and the upper bounds are computable for any N, and the limits of the sequences exist. We show that when the probability of the initial state is…

## 144 Citations

To Feed or Not to Feedback

- Computer ScienceIEEE Transactions on Information Theory
- 2014

The capacity is given for indecomposable channels without intersymbol interference as the limit of normalized directed information between the input and output sequences, maximized over an appropriate set of causally conditioned distributions.

Capacity Region of the Finite-State Multiple-Access Channel With and Without Feedback

- Computer ScienceIEEE Transactions on Information Theory
- 2009

The capacity region of the finite-state multiple-access channel (FS-MAC) with feedback that may be an arbitrary time-invariant function of the channel output samples is considered. We characterize…

Capacity of Binary Symmetric POST Channels

- Computer Science
- 2014

It is shown that the non feedback capacity of the POST(a, b) channel equals its feedback capacity, despite the memory of the channel, because the induced output distribut ion, when maximizing the directed information in the presence of feedback, can be achieved by an input distribution that does not utilize of the feedback.

Channel Capacity in the Presence of Feedback and Side Information

- Computer Science
- 2013

An inner bound is provided which demonstrates the rate required to transmit this information to the receiver in order to get a tight converse for the sum-rate capacity of the Shannon-theoretic fundamental limits of channel coding.

Coding with frame synchronization for finite-state channels with feedback

- Computer Science2009 IEEE Information Theory Workshop
- 2009

This work characterize a large family of indecomposable FSCs for which the channel state is determined by a finite number of the most recent channel inputs and outputs and derive their feedback capacity, and shows that the feedback capacity of these channels is independent of the initial channel state.

Feedback Capacity of Finite-State Channels with Causal State Known at the Encoder

- Computer Science2020 IEEE International Symposium on Information Theory (ISIT)
- 2020

A single-letter computable lower bound is derived based on auxiliary directed graphs that are used to provide an auxiliary structure for the channel outputs and are called Q-graphs, with achievable rates that outperform the best achievable rates known in the literature.

Finite-State Channel with Feedback and Causal State Information Available at the Encoder

- Computer Science2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2018

It is shown that the achievable rate can be formulated as an infinite-horizon average-reward Markov decision process (MDP), and the MDP formulation constitutes a rigorous tool to numerically compute and analytically prove achievable rates.

Upper Bounds on the Capacities of Noncontrollable Finite-State Channels With/Without Feedback

- Computer ScienceIEEE Transactions on Information Theory
- 2012

This paper takes the delayed channel state as part of the channel input and then defines the directed information rate from the new channel input to the channel output sequence to derive a series of upper bounds on the capacities of noncontrollable FSCs with/without feedback.

Capacity results on the finite state Markov wiretap channel with delayed state feedback

- Computer Science2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2017

This paper measures the eavesdropper's uncertainty about the transmitted message by equivocation, and provides inner and outer bounds on the capacity-equivocation region of this novel model, and shows that these bounds meet if the channel output for the eavesdrop is a degraded version of that for the legitimate receiver.

Capacity of a POST Channel With and Without Feedback

- Computer ScienceIEEE Transactions on Information Theory
- 2014

It is shown that the nonfeedback capacity of the POST(α) channel equals its feedback capacity, despite the memory of the channel, and that, in general, feedback may increase the capacity of a POST channel.

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