TY - GEN
T1 - Polarization of the Rényi information dimension for single and multi terminal analog compression
AU - Haghighatshoar, Saeid
AU - Abbe, Emmanuel
PY - 2013
Y1 - 2013
N2 - This paper shows that the Rényi information dimension (RID) of an i.i.d. sequence of mixture random variables polarizes to the extremal values of 0 and 1 (fully discrete and continuous distributions) when transformed by an Hadamard matrix. This provides a natural counter-part over the reals of the entropy polarization phenomenon over finite fields. It is further shown that the polarization pattern of the RID is equivalent to the BEC polarization pattern, which admits a closed form expression. These results are used to construct universal and deterministic partial Hadamard matrices for analog to analog (A2A) compression of memoryless sources. In addition, a framework for the A2A compression of multi-terminal correlated sources is developed, providing a first counter-part of the Slepian-Wolf coding problem in the A2A setting.
AB - This paper shows that the Rényi information dimension (RID) of an i.i.d. sequence of mixture random variables polarizes to the extremal values of 0 and 1 (fully discrete and continuous distributions) when transformed by an Hadamard matrix. This provides a natural counter-part over the reals of the entropy polarization phenomenon over finite fields. It is further shown that the polarization pattern of the RID is equivalent to the BEC polarization pattern, which admits a closed form expression. These results are used to construct universal and deterministic partial Hadamard matrices for analog to analog (A2A) compression of memoryless sources. In addition, a framework for the A2A compression of multi-terminal correlated sources is developed, providing a first counter-part of the Slepian-Wolf coding problem in the A2A setting.
KW - Analog compression
KW - Compressed sensing
KW - Distributed analog compression
KW - Information preserving matrices
KW - Polarization
KW - Rényi information dimension
UR - http://www.scopus.com/inward/record.url?scp=84890334547&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84890334547&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2013.6620332
DO - 10.1109/ISIT.2013.6620332
M3 - Conference contribution
AN - SCOPUS:84890334547
SN - 9781479904464
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 779
EP - 783
BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013
T2 - 2013 IEEE International Symposium on Information Theory, ISIT 2013
Y2 - 7 July 2013 through 12 July 2013
ER -