TY - GEN

T1 - Capacity of the vector Gaussian channel in the small amplitude regime

AU - Dytso, Alex

AU - Poor, H. Vincent

AU - Shitz, Shlomo Shamai

PY - 2019/1/15

Y1 - 2019/1/15

N2 - This paper studies the capacity of an ndimensional 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 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 R ¯ n scales as √n and the exact limit of √R ¯n/ √n is found.

AB - This paper studies the capacity of an ndimensional 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 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 R ¯ n scales as √n and the exact limit of √R ¯n/ √n is found.

UR - http://www.scopus.com/inward/record.url?scp=85062086222&partnerID=8YFLogxK

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U2 - 10.1109/ITW.2018.8613508

DO - 10.1109/ITW.2018.8613508

M3 - Conference contribution

AN - SCOPUS:85062086222

T3 - 2018 IEEE Information Theory Workshop, ITW 2018

BT - 2018 IEEE Information Theory Workshop, ITW 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 IEEE Information Theory Workshop, ITW 2018

Y2 - 25 November 2018 through 29 November 2018

ER -