TY - GEN

T1 - Lossy compression of decimated Gaussian random walks

AU - Murray, Georgia

AU - Kipnis, Alon

AU - Goldsmith, Andrea J.

N1 - Publisher Copyright:
© 2018 IEEE.

PY - 2018/5/21

Y1 - 2018/5/21

N2 - We consider the problem of estimating a Gaussian random walk from a lossy compression of its decimated version. Hence, the encoder operates on the decimated random walk, and the decoder estimates the original random walk from its encoded version under a mean squared error (MSE) criterion. It is well-known that the minimal distortion in this problem is attained by an estimate-and-compress (EC) source coding strategy, in which the encoder first estimates the original random walk and then compresses this estimate subject to the bit constraint. In this work, we derive a closed-form expression for this minimal distortion as a function of the bitrate and the decimation factor. Next, we consider a compress-and-estimate (CE) source coding scheme, in which the encoder first compresses the decimated sequence subject to an MSE criterion (with respect to the decimated sequence), and the original random walk is estimated only at the decoder. We evaluate the distortion under CE in a closed form and show that there exists a non-zero gap between the distortion under the two schemes. This difference in performance illustrates the importance of having the decimation factor at the encoder.

AB - We consider the problem of estimating a Gaussian random walk from a lossy compression of its decimated version. Hence, the encoder operates on the decimated random walk, and the decoder estimates the original random walk from its encoded version under a mean squared error (MSE) criterion. It is well-known that the minimal distortion in this problem is attained by an estimate-and-compress (EC) source coding strategy, in which the encoder first estimates the original random walk and then compresses this estimate subject to the bit constraint. In this work, we derive a closed-form expression for this minimal distortion as a function of the bitrate and the decimation factor. Next, we consider a compress-and-estimate (CE) source coding scheme, in which the encoder first compresses the decimated sequence subject to an MSE criterion (with respect to the decimated sequence), and the original random walk is estimated only at the decoder. We evaluate the distortion under CE in a closed form and show that there exists a non-zero gap between the distortion under the two schemes. This difference in performance illustrates the importance of having the decimation factor at the encoder.

KW - Gaussian random walk

KW - Indirect source coding

KW - Wiener process

UR - http://www.scopus.com/inward/record.url?scp=85048577467&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048577467&partnerID=8YFLogxK

U2 - 10.1109/CISS.2018.8362283

DO - 10.1109/CISS.2018.8362283

M3 - Conference contribution

AN - SCOPUS:85048577467

T3 - 2018 52nd Annual Conference on Information Sciences and Systems, CISS 2018

SP - 1

EP - 6

BT - 2018 52nd Annual Conference on Information Sciences and Systems, CISS 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 52nd Annual Conference on Information Sciences and Systems, CISS 2018

Y2 - 21 March 2018 through 23 March 2018

ER -