EE Seminar: Distributed Source Simulation With No Communication
Speaker: Tomer Berg
M.Sc. student under the supervision of Dr. Ofer Shayevitz
Sunday, March 10th, 2019 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering
Distributed Source Simulation With No Communication
Abstract
We consider the problem of distributed source simulation with no communication, in which Alice and Bob observe sequences 
and 
respectively, drawn from a joint distribution 
, and wish to locally generate sequences 
and 
respectively with a joint distribution that is close (in KL divergence) to 
. We provide a new single-letter condition under which such a simulation is asymptotically possible with a vanishing KL divergence. The Gàcs-Körner (GK) common information, which measures the amount of common randomness that can be separately extracted from either marginal of two correlated random variables, plays a crucial part in the problem of distributed source simulation: Our condition is nontrivial only in the case where the Gàcs-Körner (GK) common information between 
and 
is nonzero, and we conjecture that only scalar Markov chains 
can be simulated otherwise.
Motivated by this conjecture, we further examine the case where both 
and 
are doubly symmetric binary sources with parameters 
respectively. This is a private case of zero Gàcs-Körner (GK) common information between and . While it is trivial that in this case 
is both necessary and sufficient, we show that when 
is close to 
then any successful simulation is close to being scalar in the total variation sense.
