
Coordination Using Individually Shared Randomness
Two processors output correlated sequences using the help of a coordinat...
read it

The Capacity of Anonymous Communications
We consider the communication scenario where K transmitters are each con...
read it

Lower Bounds and a NearOptimal Shrinkage Estimator for Least Squares using Random Projections
In this work, we consider the deterministic optimization using random pr...
read it

On the Use of Randomness in Local Distributed Graph Algorithms
We attempt to better understand randomization in local distributed graph...
read it

Communication Complexity in Locally Private Distribution Estimation and Heavy Hitters
We consider the problems of distribution estimation and heavy hitter (fr...
read it

A generalization of the Von Neumann extractor
An iterative randomness extraction algorithm which generalized the Von N...
read it

Optimal Decisions of a Rational Agent in the Presence of Biased Information Providers
We consider information networks whereby multiple biasedinformationpro...
read it
How to send a real number using a single bit (and some shared randomness)
We consider the fundamental problem of communicating an estimate of a real number x∈[0,1] using a single bit. A sender that knows x chooses a value X∈0,1 to transmit. In turn, a receiver estimates x based on the value of X. We consider both the biased and unbiased estimation problems and aim to minimize the cost. For the biased case, the cost is the worstcase (over the choice of x) expected squared error, which coincides with the variance if the algorithm is required to be unbiased. We first overview common biased and unbiased estimation approaches and prove their optimality when no shared randomness is allowed. We then show how a small amount of shared randomness, which can be as low as a single bit, reduces the cost in both cases. Specifically, we derive lower bounds on the cost attainable by any algorithm with unrestricted use of shared randomness and propose nearoptimal solutions that use a small number of shared random bits. Finally, we discuss open problems and future directions.
READ FULL TEXT
Comments
There are no comments yet.