An Upper Bound to the Rate of Ideal Distributed Lossy Source Coding of Densely Sampled Data

Motivated by the question of the efficiency of dense sensor networks for sampling, encoding and reconstructing spatial random fields, this paper uses the Berger-Tung upper bound to the discrete-time distributed rate-distortion function and Grenander-Szego asymptotic eigenvalue theory to obtain an upper bound to the smallest possible rate when using distributed lossy encoding of densely spaced samples that is tighter than the bound recently obtained by Kashyap et al. Both bounds indicate that with ideal distributed lossy coding, dense sensor networks can efficiently sense and convey a field, in contrast to the negative result obtained by Marco et al. for encoders based on time- and space-invariant scalar quantization and ideal Slepian-Wolf distributed lossless coding