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Characteristic Functions and Bernoulli-Gaussian Impulsive Noise Channels

Gaerke, Tiffani M
http://rave.ohiolink.edu/etdc/view?acc_num=akron1408040080

Abstract Details

2014, Master of Science, University of Akron, Mathematics.
In this thesis, we attempt to find the necessary and sufficient conditions on the input distribution of a Bernoulli-Gaussian impulsive noise channel in order to obtain an optimal Gaussian output, maximizing the entropy capacity of the channel. We will briefly discuss the capacity of such a channel, assuming that an optimal input is available. We will derive a function which must be the characteristic function of the optimal input X if such an input exists. We then begin to validate the characteristic function. To do so, we will examine some of the necessary and sufficient conditions for determining whether a given function is a characteristic function. In particular, we give a rigorous proof that a radial function is a characteristic function of some random variable if and only if it is a completely monotone function. We then employ the property of complete monotonicity to establish a concrete necessary and sufficient condition for obtaining the optimal Gaussian output. Using this, we also identify some cases when the Bernoulli-Gaussian impulsive noise channel never has the Gaussian distribution as an output.
Truyen Nguyen, Dr. (Advisor)
Dmitry Golovaty, Dr. (Committee Member)
J. Patrick Wilber, Dr. (Committee Member)
59 p.
Electrical Engineering; Mathematics; Statistics
Characteristic function; criterion of characteristic functions; electrical engineering;

Recommended Citations

Citations

  • Gaerke, T. M. (2014). Characteristic Functions and Bernoulli-Gaussian Impulsive Noise Channels [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1408040080

    APA Style (7th edition)

  • Gaerke, Tiffani. Characteristic Functions and Bernoulli-Gaussian Impulsive Noise Channels. 2014. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1408040080.

    MLA Style (8th edition)

  • Gaerke, Tiffani. "Characteristic Functions and Bernoulli-Gaussian Impulsive Noise Channels." Master's thesis, University of Akron, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1408040080

    Chicago Manual of Style (17th edition)

akron1408040080
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This open access ETD is published by University of Akron and OhioLINK.