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On the Capacity of the Peak Power Constrained Vector Gaussian Channel: An Estimation Theoretic Perspective.
- Source :
-
IEEE Transactions on Information Theory . Jun2019, Vol. 65 Issue 6, p3907-3921. 15p. - Publication Year :
- 2019
-
Abstract
- This paper studies the capacity of an $n$ -dimensional vector Gaussian noise channel subject to the constraint that an input must lie in the ball of radius $R$ centered at the origin. It is known that in this setting, the optimizing input distribution is supported on a finite number of concentric spheres. However, the number, the positions, and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint $R$ , such that the input distribution supported on a single sphere is optimal. The maximum $\bar {R}_{n}$ , such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that $\bar {R}_{n}$ scales as $\sqrt {n}$ and the exact limit of $\frac {\bar {R}_{n}}{\sqrt {n}}$ is found. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 136543510
- Full Text :
- https://doi.org/10.1109/TIT.2018.2890208