TY - GEN
T1 - On the minimum mean p-th error in Gaussian noise channels and its applications
AU - Dytso, Alex
AU - Bustin, Ronit
AU - Tuninetti, Daniela
AU - Devroye, Natasha
AU - Poor, H. Vincent
AU - Shitz, Shlomo Shamai
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - The problem of estimating an arbitrary random variable from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the minimum mean p-th error (MMPE), is considered. The classical minimum mean square error (MMSE) is a special case of the MMPE. Several bounds and properties of the MMPE are derived and discussed. As applications of the new MMPE bounds, this paper presents: (a) a new upper bound for the MMSE that complements the 'single-crossing point property' for all SNR values below a certain value at which the MMSE is known, (b) an improved characterization of the phase-transition phenomenon which manifests, in the limit as the length of the capacity achieving code goes to infinity, as a discontinuity of the MMSE, and (c) new bounds on the second derivative of mutual information, or the first derivative of MMSE, that tighten previously known bounds.
AB - The problem of estimating an arbitrary random variable from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the minimum mean p-th error (MMPE), is considered. The classical minimum mean square error (MMSE) is a special case of the MMPE. Several bounds and properties of the MMPE are derived and discussed. As applications of the new MMPE bounds, this paper presents: (a) a new upper bound for the MMSE that complements the 'single-crossing point property' for all SNR values below a certain value at which the MMSE is known, (b) an improved characterization of the phase-transition phenomenon which manifests, in the limit as the length of the capacity achieving code goes to infinity, as a discontinuity of the MMSE, and (c) new bounds on the second derivative of mutual information, or the first derivative of MMSE, that tighten previously known bounds.
UR - http://www.scopus.com/inward/record.url?scp=84985991413&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84985991413&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2016.7541578
DO - 10.1109/ISIT.2016.7541578
M3 - Conference contribution
AN - SCOPUS:84985991413
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1646
EP - 1650
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -