How to send a real number using a single bit (and some shared randomness)

10/05/2020
by   Ran Ben Basat, et al.
0

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 worst-case (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 near-optimal solutions that use a small number of shared random bits. Finally, we discuss open problems and future directions.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/08/2018

Coordination Using Individually Shared Randomness

Two processors output correlated sequences using the help of a coordinat...
04/04/2018

The Capacity of Anonymous Communications

We consider the communication scenario where K transmitters are each con...
06/15/2020

Lower Bounds and a Near-Optimal Shrinkage Estimator for Least Squares using Random Projections

In this work, we consider the deterministic optimization using random pr...
06/02/2019

On the Use of Randomness in Local Distributed Graph Algorithms

We attempt to better understand randomization in local distributed graph...
01/07/2021

A generalization of the Von Neumann extractor

An iterative randomness extraction algorithm which generalized the Von N...
04/21/2019

Communication for Generating Correlation: A Survey

The task of manipulating correlated random variables in a distributed se...
04/27/2020

Optimal Decisions of a Rational Agent in the Presence of Biased Information Providers

We consider information networks whereby multiple biased-information-pro...