TY - GEN
T1 - MMSE dimension
AU - Wu, Yihong
AU - Verdú, Sergio
PY - 2010
Y1 - 2010
N2 - If N is standard Gaussian, the minimum mean-square error (MMSE) of estimating X based on √snrX + N vanishes at least as fast as 1/snr as snr → ∞. We define the MMSE dimension of X as thelimit as snr → ∞ of the product of snr and the MMSE. For discrete, absolutely continuous or mixed X we show that the MMSE dimension equals Renyi's information dimension. However, for singular X, we show that the product of snr and MMSE oscillates around information dimension periodically in snr (dB). We also show that discrete side information does not reduce MMSE dimension. These results extend considerably beyond Gaussian N under various technical conditions.
AB - If N is standard Gaussian, the minimum mean-square error (MMSE) of estimating X based on √snrX + N vanishes at least as fast as 1/snr as snr → ∞. We define the MMSE dimension of X as thelimit as snr → ∞ of the product of snr and the MMSE. For discrete, absolutely continuous or mixed X we show that the MMSE dimension equals Renyi's information dimension. However, for singular X, we show that the product of snr and MMSE oscillates around information dimension periodically in snr (dB). We also show that discrete side information does not reduce MMSE dimension. These results extend considerably beyond Gaussian N under various technical conditions.
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U2 - 10.1109/ISIT.2010.5513599
DO - 10.1109/ISIT.2010.5513599
M3 - Conference contribution
AN - SCOPUS:77955673443
SN - 9781424469604
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1463
EP - 1467
BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
T2 - 2010 IEEE International Symposium on Information Theory, ISIT 2010
Y2 - 13 June 2010 through 18 June 2010
ER -