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Distortion-Rate Function for Undersampled Gaussian Processes

By Iñaki Estella Aguerri, Deniz Gündüz, Andrea J. Goldsmith and Yonina Eldar


PAPER AWARD ” We study the fundamental limits in acquisition and transmission of a stationary Gaussian continuoustime process corrupted by noise. The analog signal is digitized into discrete samples with a general analog to digital (A/D) converter that prefilters the continuous process followed by a pointwise sampler. We assume that the sampler, which is not necessarily uniform, is constrained to some fixed sampling rate. The samples are then compressed and transmitted at rate R such that the distortion between the original source and its reconstruction at the receiver is minimized. We first model this problem as a remote source coding problem and characterize the remote distortion-rate function for a fixed A/D converter. We then find the minimum distortion for some fixed sampling structures. We show that uniform sampling is suboptimal in general, and multibranch sampling achieves strictly lower distortion values. Finally, we show that if the sampling rate is sufficiently high, then multibranch sampling achieves the lower bound on the distortion obtained by assuming that the noisy process is directly available at the encoder. I

Year: 2014
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