The CEO problem [multiterminal source coding]

We consider a new problem in multiterminal source coding motivated by the following decentralized communication/estimation task. A firm's Chief Executive Officer (CEO) is interested in the data sequence {X(t)} _t=1^∞ which cannot be observed directly, perhaps because it represents tactical decisions by a competing firm. The CEO deploys a team of L agents who observe independently corrupted versions of {X(t)}_t=1^∞. Because {X(t)} is only one among many pressing matters to which the CEO must attend, the combined data rate at which the agents may communicate information about their observations to the CEO is limited to, say, R bits per second. If the agents were permitted to confer and pool their data, then in the limit as L→∞ they usually would be able to smooth out their independent observation noises entirely. Then they could use their R bits per second to provide the CEO with a representation of {X(t)} with fidelity D(R), where D(·) is the distortion-rate function of {X(t)}. In particular, with such data pooling D can be made arbitrarily small if R exceeds the entropy rate H of {X(t)}. Suppose, however, that the agents are not permitted to convene, Agent i having to send data based solely on his own noisy observations {Y_i(t)}. We show that then there does not exist a finite value of R for which even infinitely many agents can make D arbitrarily small. Furthermore, in this isolated-agents case we determine the asymptotic behavior of the minimal error frequency in the limit as L and then R tend to infinity