TY - GEN

T1 - An Orthogonality Principle for Select-Maximum Estimation of Exponential Variables

AU - Erez, Uri

AU - Ostergaard, Jan

AU - Zamir, Ram

N1 - Publisher Copyright:
© 2021 IEEE.

PY - 2021/7/12

Y1 - 2021/7/12

N2 - Motivated by multiple-description source coding with feedback, it was recently proposed to encode the one-sided exponential source X via K parallel channels, Y_{1}, \ldots, Y_{K}, such that the error signals X-Y_{i}, i=1, \ldots, K, are one-sided exponential and mutually independent given X. Moreover, it was shown that the optimal estimator \hat{Y} of the source X with respect to the one-sided error criterion, is simply given by the maximum of the outputs, i.e., \hat{Y}=\max\{Y_{1},\ldots, Y_{K}\}. In this paper, we show that the distribution of the resulting estimation error X-\hat{Y}, is equivalent to that of the optimum noise in the backward test-channel of the one-sided exponential source, i.e., it is one-sided exponentially distributed and statistically independent of the joint output Y_{1}, \ldots, Y_{K}.

AB - Motivated by multiple-description source coding with feedback, it was recently proposed to encode the one-sided exponential source X via K parallel channels, Y_{1}, \ldots, Y_{K}, such that the error signals X-Y_{i}, i=1, \ldots, K, are one-sided exponential and mutually independent given X. Moreover, it was shown that the optimal estimator \hat{Y} of the source X with respect to the one-sided error criterion, is simply given by the maximum of the outputs, i.e., \hat{Y}=\max\{Y_{1},\ldots, Y_{K}\}. In this paper, we show that the distribution of the resulting estimation error X-\hat{Y}, is equivalent to that of the optimum noise in the backward test-channel of the one-sided exponential source, i.e., it is one-sided exponentially distributed and statistically independent of the joint output Y_{1}, \ldots, Y_{K}.

UR - http://www.scopus.com/inward/record.url?scp=85115080645&partnerID=8YFLogxK

U2 - 10.1109/ISIT45174.2021.9518218

DO - 10.1109/ISIT45174.2021.9518218

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AN - SCOPUS:85115080645

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 3162

EP - 3166

BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021

Y2 - 12 July 2021 through 20 July 2021

ER -