4,021 research outputs found
Achievable and Crystallized Rate Regions of the Interference Channel with Interference as Noise
The interference channel achievable rate region is presented when the
interference is treated as noise. The formulation starts with the 2-user
channel, and then extends the results to the n-user case. The rate region is
found to be the convex hull of the union of n power control rate regions, where
each power control rate region is upperbounded by a (n-1)-dimensional
hyper-surface characterized by having one of the transmitters transmitting at
full power. The convex hull operation lends itself to a time-sharing operation
depending on the convexity behavior of those hyper-surfaces. In order to know
when to use time-sharing rather than power control, the paper studies the
hyper-surfaces convexity behavior in details for the 2-user channel with
specific results pertaining to the symmetric channel. It is observed that most
of the achievable rate region can be covered by using simple On/Off binary
power control in conjunction with time-sharing. The binary power control
creates several corner points in the n-dimensional space. The crystallized rate
region, named after its resulting crystal shape, is hence presented as the
time-sharing convex hull imposed onto those corner points; thereby offering a
viable new perspective of looking at the achievable rate region of the
interference channel.Comment: 28 pages, 12 figures, to appear in IEEE Transactions of Wireless
Communicatio
On Gromov's Waist of the Sphere Theorem
The goal of this paper is to give a detailed and complete proof of M.
Gromov's waist of the sphere theorem.Comment: 34 pages, 1 figur
Generalized compactness in linear spaces and its applications
The class of subsets of locally convex spaces called -compact sets is
considered. This class contains all compact sets as well as several noncompact
sets widely used in applications. It is shown that many results well known for
compact sets can be generalized to -compact sets. Several examples are
considered.
The main result of the paper is a generalization to -compact convex sets
of the Vesterstrom-O'Brien theorem showing equivalence of the particular
properties of a compact convex set (s.t. openness of the mixture map, openness
of the barycenter map and of its restriction to maximal measures, continuity of
a convex hull of any continuous function, continuity of a convex hull of any
concave continuous function). It is shown that the Vesterstrom-O'Brien theorem
does not hold for pointwise -compact convex sets defined by the slight
relaxing of the -compactness condition. Applications of the obtained
results to quantum information theory are considered.Comment: 27 pages, the minor corrections have been mad
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