Venkataramanan, R and Tatikonda, S *The Rate-Distortion Function and Excess-Distortion Exponent of Sparse Regression Codes with Optimal Encoding.* IEEE Transactions on Information Theory, Vol. 63, no. 8, pp. 5228-5243 (August 2017). (Unpublished)

## Abstract

This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords 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 codewords 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.

Item Type: | Article |
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Uncontrolled Keywords: | cs.IT cs.IT math.IT math.ST stat.TH |

Subjects: | UNSPECIFIED |

Divisions: | Div F > Signal Processing and Communications |

Depositing User: | Cron Job |

Date Deposited: | 17 Jul 2017 19:55 |

Last Modified: | 12 Oct 2017 01:50 |

DOI: |