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Simultaneous Communication and Control

P. Whittle and J. F. Rudge
Advances in Applied Probability
Vol. 8, No. 2 (Jun., 1976), pp. 365-384
DOI: 10.2307/1425909
Stable URL: http://www.jstor.org/stable/1425909
Page Count: 20
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Simultaneous Communication and Control
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Abstract

A dynamic co-operative two-person game with imperfect information is considered, in which the conflicting aspects of an optimal policy (choice of actions to minimise 'own cost', and choice of actions to optimise communication of information) can to a large extent be decoupled and solved separately. In deriving a strategy which is asymptotically optimal (in a sense explained) we derive formulae for the capacity of a vector Gaussian channel and the rate-distortion of a vector Gaussian source. It is shown that the optimal strategy is in general non-linear in observables, but a numerical example shows that, at least in one rather special but non-trivial case, the best linear strategy may be very nearly optimal. This conclusion is made explicit by the analysis of Section 7.

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