Abstract
In this paper, we present upper bounds for the rate distortion function (RDF) of finite-length data blocks of Gaussian wide sense stationary (WSS) sources and we propose coding strategies to achieve such bounds. In order to obtain those bounds, we previously derive new results on the discrete Fourier transform (DFT) of WSS processes.
Highlights
In [1], Pearl gave an upper bound for the rate distortion function (RDF) of finite-length data blocks of Gaussian wide sense stationary (WSS) sources and proved that such bound tends to the RDF of the source when the size of the data block grows
We present two new upper bounds for the RDF of finite-length data blocks of Gaussian WSS sources and we propose coding strategies to achieve these two bounds for a given block length
Since our bounds are tighter than the one given by Pearl, they tend to the RDF of the source when the size of the data block grows
Summary
In [1], Pearl gave an upper bound for the rate distortion function (RDF) of finite-length data blocks of Gaussian wide sense stationary (WSS) sources and proved that such bound tends to the RDF of the source when the size of the data block grows He did not give a coding strategy to achieve his bound for a given block length. We present two new upper bounds for the RDF of finite-length data blocks of Gaussian WSS sources and we propose coding strategies to achieve these two bounds for a given block length. We present a numerical example to illustrate the difference between Pearl’s bound and our bounds
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