The quadratic Gaussian CEO problem

The following problem in multiterminal source coding was introduced in Berger and Zhang (see 1994 IEEE International Symposium on Information Theory, Trondheim, Norway). A firm´s CEO is interested in a data sequence {X(t)}^∞_t=1 which cannot be observed directly. The CEO em ploys a team of L agents who observe independently corrupted versions of{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. Breger et al. determine the asymptotic behavior of the minimal error frequency in the limit as L and R tend to infinity. Their result is for discrete memoryless source and observations. We consider a special case of the continuous source and observations problem. We assume that the source is an i.i.d sequence of zero mean Gaussian random variables (𝒩(0,σ²_X)) and the observations are corrupted by identical independent memoryless Gaussian noise (𝒩(0,σ²_N)). The CEO is interested in reconstructing the source with minimum mean squared error. We study the asymptotic behavior of the minimum achievable distortion in the limit as first L and then R tends to infinity