dc.contributor.author | Eisen, Jonah Sean | |
dc.date.accessioned | 2021-08-25 17:09:51 (GMT) | |
dc.date.available | 2021-08-25 17:09:51 (GMT) | |
dc.date.issued | 2021-08-25 | |
dc.date.submitted | 2021-08-18 | |
dc.identifier.uri | http://hdl.handle.net/10012/17256 | |
dc.description.abstract | We investigate the support of the capacity-achieving input distribution to a vector-valued
Gaussian noise channel. The input is subject to a radial even-moment constraint and, in some
cases, is additionally restricted to a given compact subset of R^n. Unlike much of the prior work
in this field, the noise components are permitted to have different variances and the compact
input alphabet is not necessarily a ball. Therefore, the problem considered here is not limited to
being spherically symmetric, which forces the analysis to be done in n dimensions.
In contrast to a commonly held belief, we demonstrate that the n-dimensional (real-analytic)
Identity Theorem can be used to obtain results in a multivariate setting. In particular, it is determined that when the even-moment constraint is greater than n, or when the input alphabet is
compact, the capacity-achieving distribution’s support has Lebesgue measure 0 and is nowhere
dense in R^n. An alternate proof of this result is then given by exploiting the geometry of the zero
set of a real-analytic function. Furthermore, this latter approach is used to show that the support
is composed of a countable union of submanifolds, each with dimension n − 1 or less. In the
compact case, the support is a finite union of submanifolds. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | information theory | en |
dc.subject | Gaussian noise | en |
dc.subject | vector-valued channels | en |
dc.subject | channel capacity | en |
dc.subject | capacity-achieving input distribution | en |
dc.subject | amplitude constraint | en |
dc.subject | even moment constraint | en |
dc.title | On Capacity-Achieving Input Distributions to Additive Vector Gaussian Noise Channels Under Peak and Even Moment Constraints | en |
dc.type | Master Thesis | en |
dc.pending | false | |
uws-etd.degree.department | Electrical and Computer Engineering | en |
uws-etd.degree.discipline | Electrical and Computer Engineering | en |
uws-etd.degree.grantor | University of Waterloo | en |
uws-etd.degree | Master of Applied Science | en |
uws-etd.embargo.terms | 0 | en |
uws.contributor.advisor | Mazumdar, Ravi | |
uws.contributor.advisor | Mitran, Patrick | |
uws.contributor.affiliation1 | Faculty of Engineering | en |
uws.published.city | Waterloo | en |
uws.published.country | Canada | en |
uws.published.province | Ontario | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |