TY - GEN

T1 - Universal lossy compression under logarithmic loss

AU - Shkel, Yanina

AU - Raginsky, Maxim

AU - Verdú, Sergio

N1 - Funding Information:
This work was supported by the Center for Science of Information (CSoI), an NSF Science and Technology Center, under grant agreement CCF-0939370.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - Universal lossy source coding with the logarithmic loss distortion criterion is studied. Bounds on the non-asymptotic fundamental limit of fixed-length universal coding with respect to a family of distributions are derived. These bounds generalize the well-known minimax bounds for universal lossless source coding. The asymptotic behavior of the resulting optimization problem is studied for a family of i.i.d. sources with a finite alphabet size, and is characterized up to a constant. The redundancy of memoryless sources behaves like k/2 log n, where n is the blocklength and k is the number of degrees of freedom in the parameter space. The impact of the coding rate is on the constant term: higher compression rate effectively reduces the volume of the parameter uncertainty set.

AB - Universal lossy source coding with the logarithmic loss distortion criterion is studied. Bounds on the non-asymptotic fundamental limit of fixed-length universal coding with respect to a family of distributions are derived. These bounds generalize the well-known minimax bounds for universal lossless source coding. The asymptotic behavior of the resulting optimization problem is studied for a family of i.i.d. sources with a finite alphabet size, and is characterized up to a constant. The redundancy of memoryless sources behaves like k/2 log n, where n is the blocklength and k is the number of degrees of freedom in the parameter space. The impact of the coding rate is on the constant term: higher compression rate effectively reduces the volume of the parameter uncertainty set.

UR - http://www.scopus.com/inward/record.url?scp=85034037332&partnerID=8YFLogxK

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U2 - 10.1109/ISIT.2017.8006710

DO - 10.1109/ISIT.2017.8006710

M3 - Conference contribution

AN - SCOPUS:85034037332

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1157

EP - 1161

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -