On the CEO problem

A firm´s chief executive officer (CEO) is interested in, amongst other things, the data sequence {X(t)}_t=1^∞. This data sequence cannot be observed directly, perhaps because it represents tactical decisions by a competitor of the firm. The CEO deploys a team of 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 bps. If the agents were permitted to conference and decide what to send to the CEO on the basis of their pooled data, then in the limit as L→∞ they usually would be able to smooth out their independent noises entirely and thereby allow the CEO to achieve a fidelity of D(R), where D(·) is the distortion- rate function of {X(t)}. In particular, with data pooling D can be made arbitrarily small if R exceeds the entropy rate 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)}. The authors show that there does not exist a finite value of the total data rate R for which even infinitely many agents, if they are not permitted to convene, can make D arbitrarily small. Furthermore, in this isolated-agents case they determine the asymptotic behavior of the minimal error frequency in the limit as R and then L tend to infinity