TY - GEN

T1 - An Upper Bound on the Number of Mass Points in the Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel

AU - Yagli, Semih

AU - Dytso, Alex

AU - Poor, H. Vincent

AU - Shamai Shitz, Shlomo

N1 - Funding Information:
The work of S. Yagli, A. Dytso and H. V. Poor has been supported by the U.S. National Science Foundation under Grants CCF-0939370 and CCF-1513915. The work of S. Shamai has been supported by the European Union's Horizon 2020 Research And Innovation Programme, grant agreement no. 694630.
Funding Information:
The work of S. Yagli, A. Dytso and H. V. Poor has been supported by the U.S. National Science Foundation under Grants CCF-0939370 and CCF-1513915. The work of S. Shamai has been supported by the European Union’s Horizon 2020 Research And Innovation Programme, grant agreement no. 694630.
Publisher Copyright:
© 2019 IEEE.

PY - 2019/7

Y1 - 2019/7

N2 - This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, the capacity-achieving input distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of shells of the optimal input distribution nor a bound on it was available.This paper provides an alternative proof of the finiteness of the number shells of the capacity-achieving input distribution and produces the first firm upper bound on the number of shells, paving an alternative way for approaching many such problems. In particular, for every dimension n, it is shown that the number of shells is given by O(A2) where A is the constraint on the input amplitude. Moreover, this paper also provides bounds on the number of points for the case of n = 1 with an additional power constraint.

AB - This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, the capacity-achieving input distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of shells of the optimal input distribution nor a bound on it was available.This paper provides an alternative proof of the finiteness of the number shells of the capacity-achieving input distribution and produces the first firm upper bound on the number of shells, paving an alternative way for approaching many such problems. In particular, for every dimension n, it is shown that the number of shells is given by O(A2) where A is the constraint on the input amplitude. Moreover, this paper also provides bounds on the number of points for the case of n = 1 with an additional power constraint.

UR - http://www.scopus.com/inward/record.url?scp=85073162595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073162595&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2019.8849318

DO - 10.1109/ISIT.2019.8849318

M3 - Conference contribution

AN - SCOPUS:85073162595

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1907

EP - 1911

BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019

Y2 - 7 July 2019 through 12 July 2019

ER -