Coordination Coding with Causal Decoder for Vector-valued Witsenhausen Counterexample Setups

Tobias Oechtering (1) , Mael Le Treust (2)

1 KTH - KTH Royal Institute of Technology [Stockholm]
2 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes

The vector-valued extension of the famous Witsen-hausen counterexample setup is studied where the first decision maker (DM1) non-causally knows and encodes the iid state sequence and the second decision maker (DM2) causally estimates the interim state. The coding scheme is transferred from the finite alphabet coordination problem for which it is proved to be optimal. The extension to the Gaussian setup is based on a non-standard weak typicality approach and requires a careful average estimation error analysis since the interim state is estimated by the decoder. Next, we provide a choice of auxiliary random variables that outperforms any linear scheme. The optimal scheme remains unknown.

Domaines: Théorie de l'information [cs.IT]; Informatique et théorie des jeux [cs.GT]; Sciences de l'information et de la communication

Tobias Oechtering, Mael Le Treust. Coordination Coding with Causal Decoder for Vector-valued Witsenhausen Counterexample Setups. IEEE Information Theory Workshop (ITW) 2019, Aug 2019, Visby, Sweden. ⟨hal-02278212⟩