TY - GEN

T1 - On additive channels with generalized Gaussian noise

AU - Dytso, Alex

AU - Bustin, Ronit

AU - Poor, H. Vincent

AU - Shitz, Shlomo Shamai

N1 - Funding Information:
The work of A. Dytso and H.V. Poor was supported by the National Science Foundation under Grants CCF-1420575 and CNS-1456793. The work of S. Shamai and R.Bustin was supported by the Unions Horizon 2020 Research and Innovation Programme Grant 694630. The contents of this article are solely the responsibility of the authors and do not necessarily represent the official views of the funding agencies.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - This paper considers a problem of communication over an additive noise channel where the noise is distributed according to a Generalized Gaussian (GG) distribution. In the first part of the paper, a number of properties of the family of GG distributions are derived which are of independent interest. For example, considerable attention is given to the properties of the characteristic function of the GG distribution. In the second part of the paper, the capacity of an additive noise channel with GG noise is considered under p-th absolute moment constraints. It is shown that, even though Shannon's upper bound is achievable in some instances, in general such achievability is not possible. Moreover, it is shown that discrete inputs can achieve capacity within a constant gap or full degree of freedom for any p-th absolute moment constraint. Following the seminal work of Smith, the paper also gives a condition under which discrete inputs are exactly optimal.

AB - This paper considers a problem of communication over an additive noise channel where the noise is distributed according to a Generalized Gaussian (GG) distribution. In the first part of the paper, a number of properties of the family of GG distributions are derived which are of independent interest. For example, considerable attention is given to the properties of the characteristic function of the GG distribution. In the second part of the paper, the capacity of an additive noise channel with GG noise is considered under p-th absolute moment constraints. It is shown that, even though Shannon's upper bound is achievable in some instances, in general such achievability is not possible. Moreover, it is shown that discrete inputs can achieve capacity within a constant gap or full degree of freedom for any p-th absolute moment constraint. Following the seminal work of Smith, the paper also gives a condition under which discrete inputs are exactly optimal.

UR - http://www.scopus.com/inward/record.url?scp=85028505094&partnerID=8YFLogxK

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U2 - 10.1109/ISIT.2017.8006563

DO - 10.1109/ISIT.2017.8006563

M3 - Conference contribution

AN - SCOPUS:85028505094

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 426

EP - 430

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -