Abstract
In this paper, rate distortion performance of nested sampling and coprime sampling is studied. It is shown that with the increasing of distortion, the data rate decreases. With these two sparse sampling algorithms, the data rate is proved to be much less than that without sparse sampling. With the increasing of sampling spacings, the data rate decreases at certain distortion, which is because with more sparse sampling, less number of bits is required to represent the information. We also prove that with the same sampling pairs, the rate of nested sampling is less than that of coprime sampling at the same distortion. The reason is that nested sampling collects a little less number of samples than coprime sampling with the same length of data, which is a little sparser than coprime sampling.
Highlights
The twenty-first century is awash with data
Information rate distortion function is a measure of distortion between the original source and its representation
With the increasing of sampling spacings, the data rate decreases at certain distortion, which is because with more sparse sampling, less number of bits is required to represent the information
Summary
The twenty-first century is awash with data. Data are flooding in at rates never seen before, doubling almost every 18 months [1], as result of new information gathered from Radar, Web communities, newly deployed smart assets, and customer data from public, proprietary, purchased sources, and so forth. The authors in [8] have already proved that these two sets of samples of the signal could fully estimate all lags of autocorrelation of the original signal As both nested sampling and coprime sampling could keep the statistical property of the original signal, these two sampling algorithms could be applied to Big Data to highly reduce the transmission or storage cost of Big Data. We will provide theoretical rate distortion performance, because of these two sparse sampling algorithms, either nested sampling (NS) or coprime sampling (CS). With the increasing of sampling spacings, the data rate decreases at certain distortion, which is because with more sparse sampling, less number of bits is required to represent the information. Theoretical derivation of rate distortion performance of nested sampling and coprime sampling is detailed in Sections 3.1 and 3.2.
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