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The Rate-Distortion Function and Excess-Distortion Exponent of Sparse Regression Codes With Optimal Encoding.
- Source :
-
IEEE Transactions on Information Theory . Aug2017, Vol. 63 Issue 8, p5228-5243. 16p. - Publication Year :
- 2017
-
Abstract
- This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, code words are linear combinations of subsets of columns of a design matrix. It is shown that with minimum-distance encoding, sparse regression codes achieve the Shannon rate-distortion function for i.i.d. Gaussian sources R^ (D) as well as the optimal excess-distortion exponent. This completes a previous result which showed that R^ (D) and the optimal exponent were achievable for distortions below a certain threshold. The proof of the rate-distortion result is based on the second moment method, a popular technique to show that a non-negative random variable $X$ is strictly positive with high probability. In our context, $X$ is the number of code words within target distortion $D$ of the source sequence. We first identify the reason behind the failure of the standard second moment method for certain distortions, and illustrate the different failure modes via a stylized example. We then use a refinement of the second moment method to show that R^ (D) is achievable for all distortion values. Finally, the refinement technique is applied to Suen’s correlation inequality to prove the achievability of the optimal Gaussian excess-distortion exponent. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 63
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 124147939
- Full Text :
- https://doi.org/10.1109/TIT.2017.2716360