The quadratic Gaussian CEO problem

A firm´s CEO employs a team of L agents who observe independently corrupted versions of a data sequence {X(t)}_t=1^∞ . Let R be the total data rate at which the agents may communicate information about their observations to the CEO. The agents are not allowed to convene. Berger, Zhang and Viswanathan (see ibid., vol.42, no.5, p.887-902, 1996) determined the asymptotic behavior of the minimal error frequency in the limit as L and R tend to infinity for the case in which the source and observations are discrete and memoryless. We consider the same multiterminal source coding problem when {X(t)}_t=1^∞ is independent and identically distributed (i.i.d.) Gaussian random variable corrupted by independent Gaussian noise. We study, under quadratic distortion, the rate-distortion tradeoff in the limit as L and R tend to infinity. As in the discrete case, there is a significant loss between the cases when the agents are allowed to convene and when they are not. As L→∞, if the agents may pool their data before communicating with the CEO, the distortion decays exponentially with the total rate R; this corresponds to the distortion-rate function for an i.i.d. Gaussian source. However, for the case in which they are not permitted to convene, we establish that the distortion decays asymptotically only as R-l