Characterization of optimal input distributions for Gaussian-mixture noise channels

Hung V. Vu; Nghi H. Tran; Mustafa Cenk Gursoy; Tho Le-Ngoc; S. I. Hariharan

doi:10.1109/CWIT.2015.7255146

Characterization of optimal input distributions for Gaussian-mixture noise channels

Hung V. Vu, Nghi H. Tran, Mustafa Cenk Gursoy, Tho Le-Ngoc, S. I. Hariharan

Department of Electrical Engineering & Computer Science

Research output: Chapter in Book/Entry/Poem › Conference contribution

Abstract

This paper addresses the characterization of optimal input distributions for the general additive quadrature Gaussian-mixture (GM) noise channel under an average power constraint. The considered model can be used to represent a wide variety of communication channels, such as the well-known Bernoulli-Gaussian and Middleton Class-A impulsive noise channels, co-channel interference in cellular communications, and cognitive radio channels under imperfect spectrum sensing. We first demonstrate that there exists a unique input distribution achieving the channel capacity and the optimal input has an uniformly distributed phase. By using the Kuhn-Tucker conditions (KTC) and Bernstein's theorem, we then demonstrate that there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution. Equivalently, the optimal amplitude input distribution is discrete. Furthermore, by applying a novel bounding technique on the KTC, it is then shown that the optimal amplitude distribution has a finite number of mass points.

Original language	English (US)
Title of host publication	2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	32-35
Number of pages	4
ISBN (Electronic)	9781479965601
DOIs	https://doi.org/10.1109/CWIT.2015.7255146
State	Published - Sep 10 2015
Event	14th IEEE Canadian Workshop on Information Theory, CWIT 2015 - St. John's, Canada Duration: Jul 6 2015 → Jul 9 2015

Publication series

Name	2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015

Other

Other	14th IEEE Canadian Workshop on Information Theory, CWIT 2015
Country/Territory	Canada
City	St. John's
Period	7/6/15 → 7/9/15

Keywords

Capacity-achieving distribution
Discrete input
Gaussian-mixture channel
Shannon capacity

ASJC Scopus subject areas

Computer Networks and Communications
Information Systems
Software

Access to Document

10.1109/CWIT.2015.7255146

Cite this

Vu, H. V., Tran, N. H., Gursoy, M. C., Le-Ngoc, T., & Hariharan, S. I. (2015). Characterization of optimal input distributions for Gaussian-mixture noise channels. In 2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015 (pp. 32-35). Article 7255146 (2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CWIT.2015.7255146

Characterization of optimal input distributions for Gaussian-mixture noise channels. / Vu, Hung V.; Tran, Nghi H.; Gursoy, Mustafa Cenk et al.
2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 32-35 7255146 (2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015).

Research output: Chapter in Book/Entry/Poem › Conference contribution

Vu, HV, Tran, NH, Gursoy, MC, Le-Ngoc, T & Hariharan, SI 2015, Characterization of optimal input distributions for Gaussian-mixture noise channels. in 2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015., 7255146, 2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015, Institute of Electrical and Electronics Engineers Inc., pp. 32-35, 14th IEEE Canadian Workshop on Information Theory, CWIT 2015, St. John's, Canada, 7/6/15. https://doi.org/10.1109/CWIT.2015.7255146

Vu HV, Tran NH, Gursoy MC, Le-Ngoc T, Hariharan SI. Characterization of optimal input distributions for Gaussian-mixture noise channels. In 2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 32-35. 7255146. (2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015). doi: 10.1109/CWIT.2015.7255146

@inproceedings{eeed1756e79b43cc9eddd039f1dd434c,

title = "Characterization of optimal input distributions for Gaussian-mixture noise channels",

abstract = "This paper addresses the characterization of optimal input distributions for the general additive quadrature Gaussian-mixture (GM) noise channel under an average power constraint. The considered model can be used to represent a wide variety of communication channels, such as the well-known Bernoulli-Gaussian and Middleton Class-A impulsive noise channels, co-channel interference in cellular communications, and cognitive radio channels under imperfect spectrum sensing. We first demonstrate that there exists a unique input distribution achieving the channel capacity and the optimal input has an uniformly distributed phase. By using the Kuhn-Tucker conditions (KTC) and Bernstein's theorem, we then demonstrate that there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution. Equivalently, the optimal amplitude input distribution is discrete. Furthermore, by applying a novel bounding technique on the KTC, it is then shown that the optimal amplitude distribution has a finite number of mass points.",

keywords = "Capacity-achieving distribution, Discrete input, Gaussian-mixture channel, Shannon capacity",

author = "Vu, {Hung V.} and Tran, {Nghi H.} and Gursoy, {Mustafa Cenk} and Tho Le-Ngoc and Hariharan, {S. I.}",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 14th IEEE Canadian Workshop on Information Theory, CWIT 2015 ; Conference date: 06-07-2015 Through 09-07-2015",

year = "2015",

month = sep,

day = "10",

doi = "10.1109/CWIT.2015.7255146",

language = "English (US)",

series = "2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "32--35",

booktitle = "2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015",

}

TY - GEN

T1 - Characterization of optimal input distributions for Gaussian-mixture noise channels

AU - Vu, Hung V.

AU - Tran, Nghi H.

AU - Gursoy, Mustafa Cenk

AU - Le-Ngoc, Tho

AU - Hariharan, S. I.

PY - 2015/9/10

Y1 - 2015/9/10

N2 - This paper addresses the characterization of optimal input distributions for the general additive quadrature Gaussian-mixture (GM) noise channel under an average power constraint. The considered model can be used to represent a wide variety of communication channels, such as the well-known Bernoulli-Gaussian and Middleton Class-A impulsive noise channels, co-channel interference in cellular communications, and cognitive radio channels under imperfect spectrum sensing. We first demonstrate that there exists a unique input distribution achieving the channel capacity and the optimal input has an uniformly distributed phase. By using the Kuhn-Tucker conditions (KTC) and Bernstein's theorem, we then demonstrate that there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution. Equivalently, the optimal amplitude input distribution is discrete. Furthermore, by applying a novel bounding technique on the KTC, it is then shown that the optimal amplitude distribution has a finite number of mass points.

AB - This paper addresses the characterization of optimal input distributions for the general additive quadrature Gaussian-mixture (GM) noise channel under an average power constraint. The considered model can be used to represent a wide variety of communication channels, such as the well-known Bernoulli-Gaussian and Middleton Class-A impulsive noise channels, co-channel interference in cellular communications, and cognitive radio channels under imperfect spectrum sensing. We first demonstrate that there exists a unique input distribution achieving the channel capacity and the optimal input has an uniformly distributed phase. By using the Kuhn-Tucker conditions (KTC) and Bernstein's theorem, we then demonstrate that there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution. Equivalently, the optimal amplitude input distribution is discrete. Furthermore, by applying a novel bounding technique on the KTC, it is then shown that the optimal amplitude distribution has a finite number of mass points.

KW - Capacity-achieving distribution

KW - Discrete input

KW - Gaussian-mixture channel

KW - Shannon capacity

UR - http://www.scopus.com/inward/record.url?scp=84957666923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957666923&partnerID=8YFLogxK

U2 - 10.1109/CWIT.2015.7255146

DO - 10.1109/CWIT.2015.7255146

M3 - Conference contribution

AN - SCOPUS:84957666923

T3 - 2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015

SP - 32

EP - 35

BT - 2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 14th IEEE Canadian Workshop on Information Theory, CWIT 2015

Y2 - 6 July 2015 through 9 July 2015

ER -

Characterization of optimal input distributions for Gaussian-mixture noise channels

Abstract

Publication series

Other

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this