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Zero-Error Feedback Capacity for Bounded Stabilization and Finite-State Additive Noise Channels.
- Source :
-
IEEE Transactions on Information Theory . Oct2022, Vol. 68 Issue 10, p6335-6355. 21p. - Publication Year :
- 2022
-
Abstract
- This article studies the zero-error feedback capacity of causal discrete channels with memory. First, by extending the classical zero-error feedback capacity concept, a new notion of 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. Furthermore, the zero-error feedback capacity of a class of additive noise channels is investigated. It is known that for a discrete channel with correlated additive noise, the ordinary capacity with or without feedback is equal $\log q-\mathcal {H}_{ch} $ , where $\mathcal {H}_{ch} $ is the entropy rate of the noise process and $q $ is the input alphabet size. In this paper, for a class of finite-state additive noise channels (FSANCs), it is shown that the zero-error feedback capacity is either zero or $C_{0f} =\log q -h_{ch} $ , where $h_{ch} $ is the topological entropy of the noise process. A condition is given to determine when the zero-error capacity with or without feedback is zero. This, in conjunction with the stabilization result, leads to a “Small-Entropy Theorem”, stating that stabilization over FSANCs can be achieved if the sum of the topological entropies of the linear system and the channel is smaller than $\log q$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 159210742
- Full Text :
- https://doi.org/10.1109/TIT.2022.3179029