Name
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 $\overline{R}_{n}$, such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that $\overline{R}_{n}$ scales as $\sqrt{n}$ and the exact limit of $\overline{R}_{n}\overline{\sqrt{n}}$ is found. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1109/ITW.2018.8613508 | 2018 IEEE Information Theory Workshop (ITW) |
Keywords | Field | DocType |
integral equation,vector Gaussian channel,single sphere,concentric spheres,finite number,optimizing input distribution,n-dimensional vector Gaussian noise channel subject | Discrete mathematics,Finite set,Concentric,Computer science,Upper and lower bounds,Integral equation,SPHERES,Gaussian noise,Channel capacity,Amplitude | Conference |
ISSN | ISBN | Citations |
2475-420X | 978-1-5386-3600-8 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alex Dytso | 1 | 45 | 20.03 |
| H. V. Poor | 2 | 25411 | 1951.66 |
| Shlomo Shamai Shitz | 3 | 3 | 3.14 |