dc.contributor.author | Mamandipoor, Babak | |
dc.date.accessioned | 2013-01-21 19:55:40 (GMT) | |
dc.date.available | 2013-01-21 19:55:40 (GMT) | |
dc.date.issued | 2013-01-21T19:55:40Z | |
dc.date.submitted | 2013 | |
dc.identifier.uri | http://hdl.handle.net/10012/7223 | |
dc.description.abstract | Characterizing probability distribution function for the input of a communication channel that achieves the maximum possible data rate is one of the most fundamental problems in the field of information theory. In his ground-breaking paper, Shannon showed that the capacity of a point-to-point additive white Gaussian noise channel under an average power constraint at the input, is achieved by Gaussian distribution. Although imposing a limitation on the peak of the channel input is also very important in modelling the communication system more accurately, it has gained much less attention in the past few decades. A rather unexpected result of Smith indicated that the capacity achieving distribution for an AWGN channel under peak constraint at the input is unique and discrete, possessing a finite number of mass points.
In this thesis, we study multiple access channel under peak constraints at the inputs of the channel. By extending Smith's argument to our multi-terminal problem we show that any point on the boundary of the capacity region of the channel is only achieved by discrete distributions with a finite number of mass points. Although we do not claim uniqueness of the capacity-achieving distributions, however, we show that only discrete distributions with a finite number of mass points can achieve points on the boundary of the capacity region.
First we deal with the problem of maximizing the sum-rate of a two user Gaussian MAC with peak constraints. It is shown that generating the code-books of both users according to discrete distributions with a finite number of mass points achieves the largest sum-rate in the network. After that we generalize our proof to maximize the weighted sum-rate of the channel and show that the same properties hold for the optimum input distributions. This completes the proof that the capacity region of a two-user Gaussian MAC is achieved by discrete input distributions with a finite number of mass points. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | Multiple Access Channel | en |
dc.subject | Peak Constraint | en |
dc.title | Capacity-Achieving Distributions of Gaussian Multiple Access Channel with Peak Constraints | en |
dc.type | Master Thesis | en |
dc.pending | false | en |
dc.subject.program | Electrical and Computer Engineering | en |
uws-etd.degree.department | Electrical and Computer Engineering | en |
uws-etd.degree | Master of Applied Science | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |