On additive channels with generalized Gaussian noise

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.

[1]  M. Jaidane-Saidane,et al.  Modeling of the Load Duration Curve Using the Asymmetric Generalized Gaussian Distribution: Case of the Tunisian Power System , 2008, Proceedings of the 10th International Conference on Probablistic Methods Applied to Power Systems.

[2]  Norman C. Beaulieu,et al.  Designing Time-Hopping Ultrawide Bandwidth Receivers for Multiuser Interference Environments , 2009, Proceedings of the IEEE.

[3]  Denis Friboulet,et al.  Statistical modeling of the radio-frequency signal in echocardiographic images based on generalized Gaussian distribution , 2006, 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006..

[4]  Thomas M. Cover,et al.  Elements of Information Theory: Cover/Elements of Information Theory, Second Edition , 2005 .

[5]  Aaron D. Wyner,et al.  On the capacity of the Gaussian channel with a finite number of input levels , 1990, IEEE Trans. Inf. Theory.

[6]  M.S. Davis,et al.  Statistical Modeling and ML Parameter Estimation of Complex SAR Imagery , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[7]  Minh N. Do,et al.  Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance , 2002, IEEE Trans. Image Process..

[8]  Erwin Lutwak,et al.  Moment-Entropy Inequalities for a Random Vector , 2007, IEEE Transactions on Information Theory.

[9]  Shlomo Shamai,et al.  Transition points in the capacity-achieving distribution for the peak-power limited AWGN and free-space optical intensity channels , 2010, Probl. Inf. Transm..

[10]  Monika Agrawal,et al.  Underwater acoustic noise with generalized Gaussian statistics: Effects on error performance , 2013, 2013 MTS/IEEE OCEANS - Bergen.

[11]  S. Nadarajah.  A generalized normal distribution , 2005 .

[12]  Saralees Nadarajah,et al.  On the characteristic function of the generalized normal distribution , 2010 .

[13]  Shlomo Shamai,et al.  Mutual information and minimum mean-square error in Gaussian channels , 2004, IEEE Transactions on Information Theory.

[14]  Joel G. Smith,et al.  The Information Capacity of Amplitude- and Variance-Constrained Scalar Gaussian Channels , 1971, Inf. Control..

[15]  Sergio Verdu,et al.  The exponential distribution in information theory , 1996 .

[16]  John B. Thomas,et al.  Detectors for discrete-time signals in non-Gaussian noise , 1972, IEEE Trans. Inf. Theory.

[17]  Fernando Pérez-González,et al.  Modeling Gabor Coefficients via Generalized Gaussian Distributions for Face Recognition , 2007, 2007 IEEE International Conference on Image Processing.