Witsenhausen's counterexample as Assisted Interference Suppression

Authors:
Pulkit Grover;Anant Sahai
Affiliations:
Wireless Foundations, Department of EECS, University of California at Berkeley, CA 94720, USA.;Wireless Foundations, Department of EECS, University of California at Berkeley, CA 94720, USA
Venue:
International Journal of Systems, Control and Communications
Year:
2010

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Abstract

Motivated by the existence of an implicit channel in Witsenhausen's counterexample, we formulate a vector extension that can be viewed as a toy wireless communication problem "Assisted Interference Suppression" (AIS). Information-theoretic lower and upper bounds (based respectively on ideas from rate-distortion theory and dirty-paper coding) are then derived on the optimal cost and the asymptotic optimal cost is characterised to within a factor of 2 regardless of the problem parameters. Restricted to the scalar problem, it is shown that the new lower bound can be better than Witsenhausen's bound by an arbitrarily large factor.