STOCHASTIC GEOMETRY, INFORMATION THEORY AND WIRELESS NETWORKS
STOCHASTIC GEOMETRY AND INFORMATION THEORY
NETWORK INFORMATION THEORY: Analysis of interference channels in
arxiv-1102.2868 (Interference Networks with Point-to-Point Codes)
Abbas El Gamal and
ERROR EXPONENTS: A new viewpoint on Shannon's capacity and error exponents was developed in
(Information-Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements)
STOCHASTIC GEOMETRY AND CELLULAR NETWORKS
In reuse-1 cellular networks,
several base stations share the same (or different but interfering)
channel(s). In this case, the area where the signal of a given base station
can be received is the area where the signal
to interference ratio is large enough.
COVERAGE: We started studying this class of coverage problems with
(INRIA & ENS) and then Florent Tournois in
Here are the
slides of a
presentation of the first steps of this approach that was made at the
Summer Research Institute
of EPFL in July 2000.
The obtained results allowed us to compute quantities
of practical interest within this setting: for instance
the law of the number of base stations covering a given point.
Another outcome was the design of a new class of
distributed admission control protocols for large
networks using power control; this class of protocols was first presented at
POWER CONTROL: We further developped this approach
jointly with Mohamed Karray
of France Telecom R&D. The first extensions (presented at
INFOCOM 2004 )
allowed us to analyze both the up and the downlink, and
also to take the maximal power into account
INFOCOM 2005 )
allow us to evaluate the
probability that a user joining and asking for
some predefined bit rate will
be rejected by the network due to the infeasibility of
the associated power control problem
we proposed new self-organization mechanisms for power and channel selection as well as for user association
based on techniques used in statistical physics and in particular on Gibbs' sampler. The paper
Self-optimization in mobile cellular networks: power control and user association
was presented at
RATE AND COVERAGE PROBABILITY: We developed new tools with
to analyze coverage and rates in cellular networks.
The aim of this research is to derive simple closed form expressions for
these quantities that could replace the simulation tools currently used.
- The first results we obtained bear on macro cell cellular networks
and were presented at the Allerton Conference in 2010.
- The most recent results focus on multi-tier networks with
a mix of macro, pico and femto cells
and were presented at
STOCHASTIC GEOMETRY AND MOBILE AD HOC NETWORKS
- CONNECTIVITY. In the
(presented at INFOCOM 2003
and then published in IEEE Transactions on Networking in 2005),
coauthored by Olivier Dousse,
of EPFL and myself,
we studied the impact of the limitations of
information theory on the joint feasibility of a collection of
wireless channels in a mobile ad hoc network.
- MEDIUM ACCESS CONTROL. Jointly with
Bartek Blaszczyszyn (INRIA & ENS) and
Paul Muhlethaler (INRIA),
we proposed and studied a Spatial Aloha protocol
for the access to the shared medium in a mobile ad hoc network.
- POWER CONTROL. The use of power control in mobile ad hoc networks
was studied with
Nicholas Bambos and Carri Chan of Stanford
University and myself in a
paper presented at
- ROUTING. The geometry of routing was studied in the following papers:
STOCHASTIC GEOMETRY AND CSMA NETWORKS
SELF ORGANIZATION: the self organization
of interfering Wifi (802.11) access points was studied, jointly with a
group of researchers at INTEL Cambridge.
The question of interest is that of the design of fully
distributed algorithms for channel selection and access
point association. The
which proposed a new approach to this
problem based on Gibbs' sampler, was presented at
- MEDIUM ACCESS PROBABILITY: the medium access probability of CSMA was studied using point process theory in
(A Stochastic Geometry Analysis of Dense IEEE 802.11 Networks),
with Huu Quynh Nguyen and
Daniel Kofman (Infocom 2007).
COGNITIVE RADIO: CSMA based cognitive radio networks were studied with
Tien Viet Nguyen
in the paper
A Stochastic Geometry Model for Cognitive Radio Networks, published by the Computer Journal in 2011.
Last revised: July, 2011.