arXiv subjects

Amir Saberi

Publications and source records attributed to Amir Saberi.

4 recordsLinked to original sources

arXiv2022

Zero-Error Feedback Capacity for Bounded Stabilization and Finite-State Additive Noise Channels

This article studies the zero-error feedback capacity of {\em causal} discrete channels with memory. First, by extending the classical zero-error feedback capacity concept, a new notion of {\em uniform zero-error feedback capacity} $ C_{0f} $ for such channels is introduced. Using this notion a tight condition for {bounded} stabilization of unstable {noisy} linear systems via causal channels is obtained, assuming no {channel} state information at either end of the channel.

cs.IT↗

arXiv2021

Bounded State Estimation over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the {\em topological entropy} of the channel dynamics. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel.

eess.SY↗

arXiv2020

An Explicit Formula for the Zero-Error Feedback Capacity of a Class of Finite-State Additive Noise Channels

It is known that for a discrete channel with correlated additive noise, the ordinary capacity with or without feedback both equal $ \log q-\mathcal{H} (Z) $, where $ \mathcal{H}(Z) $ is the entropy rate of the noise process $ Z $ and $ q $ is the alphabet size. In this paper, a class of finite-state additive noise channels is introduced. It is shown that the zero-error feedback capacity of such channels is either zero or $C_{0f} =\log q -h (Z) $, where $ h (Z) $ is the {\em topological entropy} of the noise process. A topological condition is given when the zero-error capacity is zero, with or without feedback. Moreover, the zero-error capacity without feedback is lower-bounded by $ \log q-2 h (Z) $. We explicitly compute the zero-error feedback capacity for several examples, including channels with isolated errors and a Gilbert-Elliot channel.

cs.IT↗

arXiv2019

State Estimation over Worst-Case Erasure and Symmetric Channels with Memory

Worst-case models of erasure and symmetric channels are investigated, in which the number of channel errors occurring in each sliding window of a given length is bounded. Upper and lower bounds on their zero-error capacities are derived, with the lower bounds revealing a connection with the topological entropy of the channel dynamics. Necessary and sufficient conditions for linear state estimation with bounded estimation errors via such channels are then obtained, by extending previous results for non-stochastic memoryless channels to those with finite memory. These estimation conditions involve the topological entropies of the linear system and the channel.

eess.SP↗