62,798 research outputs found
An independence theorem for NTP2 theories
We establish several results regarding dividing and forking in NTP2 theories.
We show that dividing is the same as array-dividing. Combining it with
existence of strictly invariant sequences we deduce that forking satisfies the
chain condition over extension bases (namely, the forking ideal is S1, in
Hrushovski's terminology). Using it we prove an independence theorem over
extension bases (which, in the case of simple theories, specializes to the
ordinary independence theorem). As an application we show that Lascar strong
type and compact strong type coincide over extension bases in an NTP2 theory.
We also define the dividing order of a theory -- a generalization of Poizat's
fundamental order from stable theories -- and give some equivalent
characterizations under the assumption of NTP2. The last section is devoted to
a refinement of the class of strong theories and its place in the
classification hierarchy
Extended Generalized DoF Optimality Regime of Treating Interference as Noise in the X Channel
The simple scheme of treating interference as noise (TIN) is studied in this
paper for the 3 x 2 X channel. A new sum-capacity upper bound is derived. This
upper bound is transformed into a generalized degrees-of-freedom (GDoF) upper
bound, and is shown to coincide with the achievable GDoF of scheme that
combines TDMA and TIN for some conditions on the channel parameters. These
conditions specify a noisy interference regime which extends noisy interference
regimes available in literature. As a by-product, the sum-capacity of the 3 x 2
X channel is characterized within a constant gap in the given noisy
interference regime.Comment: 5 pages, 2 figure
Upper Bounds and Duality Relations of the Linear Deterministic Sum Capacity for Cellular Systems
The MAC-BC duality of information theory and wireless communications is an
intriguing concept for efficient algorithm design. However, no concept is known
so far for the important cellular channel. To make progress on this front, we
consider in this paper the linear deterministic cellular channel. In
particular, we prove duality of a network with two interfering MACs in each
cell and a network with two interfering BCs in each cell. The operational
region is confined to the weak interference regime. First, achievable schemes
as well as upper bounds will be provided. These bounds are the same for both
channels. We will show, that for specific cases the upper bound corresponds to
the achievable scheme and hence establishing a duality relationship between
them.Comment: 6 pages, to appear in IEEE ICC 2014, Sydney, Australi
- …