Sunday, Dec 4, 2005, 11:15-12:15
Room 309
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Guy Kindler
Microsoft Research
Title:
On Gallager's problem: new lower-bounds for noisy communication
Abstract:
The effect of noise on computation and communication has been studied
extensively in recent decades. This field of research can be traced back
to
another over a noisy channel only requires a constant blowup in resource
usage, compared to transmission over a noise free channel. Over the years
it was shown that a constant blowup is sufficient to overcome noise for
many other models.
In this talk I will discuss a model introduced by El Gamal in 1984 for
sharing information over a noisy broadcast network: each of N players is
given one input bit, and the goal is for all players to learn (with high
probability) all the input bits of the other players, using the smallest
possible number of broadcasts over a joint communication channel. In each
broadcast a player transmits one bit to all other players; however noise
flips the bit heard by each recipient with some fixed probability.
Without noise, N broadcasts would trivially suffice for the players to
learn all bits. However the best known protocol that deals with noise,
discovered by Gallager in 1988, uses $N\log\log N$ broadcasts. Attempts
made since to bring the blowup down to a constant have failed. Our main
result is that Gallager's protocol is in fact optimal up to a constant
factor.
This is joint work with Navin Goyal and Michael Saks.