Distortion sum-rate performance of successive coding strategy in Gaussian wireless sensor networks

Abstract

In this paper, we investigate the distortion sum-rate performance of the successive coding strategy in the so-called quadratic Gaussian CEO problem. In the CEO problem, the central unit or the CEO desires to obtain an optimal estimate of the source signal. Since the source cannot be observed directly, L sensors will be deployed to observe independently corrupted versions of the source. They communicate information about their observations to the CEO through rate constrained noiseless channels without cooperating with each other. We consider a distributed sensor network consisting of two sensors with different noise levels and derive the minimum achievable distortion under a sum-rate constraint using the successive coding strategy of S.C. Draper and G.W. Wornell (2004). We also demonstrate that the best way to achieve minimum distortion under a sum-rate constraint is to allocate more rate to the sensor with higher quality of observation in a generalized water-filling manner. The fractional rate allocation is approximately 1/2 if the sum-rate lowbarR is large. Thus, we can simplify rate allocation problem in a general parallel sensor network with L sensors by assigning equal rates to sensors, provided the average rate per sensor node is large. We show that this scheme may not cause a large extra distortion compared with the minimum achievable distortion. Finally, we consider the problem of combining source and channel coding in sensor networks. Two paradigms are considered, Shannon's separation paradigm and joint source-channel coding paradigm. We obtain the distortion-power tradeoffs for both coding paradigms in the Gaussian sensor network with multiple access channel