Lower bound to the AWGN remote rate-distortion function

In the remote source coding problem, an underlying source is observed in noise. The noisy observations must be encoded into a bit stream in such a way as to enable the decoder to produce a good approximation to the original source sequence. The trade-off between the rate of the bit stream and the fidelity of the reconstructed source sequence is sometimes referred to as the remote rate-distortion function. This paper focuses on a special case of the remote source coding problem: The encoder obtains M noisy versions of each underlying source sample. The probability density function of the underlying source is arbitrary, but the observation noise is assumed to be Gaussian (hence the name "AWGN remote rate-distortion function"). The goal is to reconstruct the underlying source sequence to within mean-squared error. For this scenario, a new lower bound to the rate-distortion function is presented. The investigations are motivated by a study of the fundamental performance trade-offs in certain sensor network scenarios. The presented lower bound on the remote rate-distortion function is one of the building blocks for a cut-set argument that leads to an upper bound to the performance achievable in these sensor networks.