Performance of the successive coding strategy in the CEO problem

We consider a distributed sensor network in which sensors communicate their observations to the CEO using limited transmission rate. We use successive coding strategy of S. C. Draper and G. W. Wornell (2004) and obtain the optimal distortion sum-rate tradeoff for L sensors with different noise levels. Our result is an extension of the result of S. C. Draper and G. W. Wornell (2004), where the optimal distortion sum-rate tradeoff for two equal-SNR sensors is derived. As the number of sensors increases, the achievable distortion decreases since the CEO accumulates more data and can obtain a better estimate of the source. The fraction of the total rate allocated to each sensor is approximately 1/L if the average rate per sensor node gets small or if the sum-rate _R is very large for a fixed L. Thus, we can simplify rate allocation problem in a general parallel sensor network with L sensors by assigning equal rates to sensors. We show that this scheme may not cause a large extra distortion compared with the minimum achievable distortion. Finally, we obtain a lower bound for the minimum achievable distortion in the Gaussian sensor network.