TY - JOUR

T1 - Entropy amplification property and the loss for writing on dirty paper

AU - Cohen, Aaron S.

AU - Zamir, Ram

N1 - Funding Information:
Manuscript received November 20, 2006; revised October 31, 2007. The work of A. S. Cohen was supported in part by the National Science Foundation under Grant DMS-0074276. The work of R. Zamir was performed during 2002–2003, while he was on sabbatical leave from Tel-Aviv University and a Visiting Scientist at the Signals, Information and Algorithms Group, the Research Laboratories of Electronics, the Massachusetts Institute of Technology, Cambridge. The material in this paper was presented in part at the 41st Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, October 2003, and at the IEEE International Symposium on Information Theory (ISIT04), Chicago, IL, June/July 2004.

PY - 2008/4

Y1 - 2008/4

N2 - Costa's "writing on dirty paper"(WDP) shows that the power-constrained channel Y = X + S + Z, with Gaussian Z, has the same capacity as the standard AWGN channel Y = X + Z, provided that the "interference" S (no matter how strong it is) is known at the transmitter. While this ability for perfect interference cancelation is very appealing, it relies heavily on the Gaussianity of the (unknown) noise Z. We construct an example of "bad"noise for writing on dirty paper, namely, "difference set noise". If the interference S is strong, then difference-set noise limits the WDP capacity to at most 2 bits. At the same time, like in the AWGN case, the zero-interference capacity grows without bound with the input constraint. Thus almost 100% of the available capacity is lost in WDP in the presence of difference-set noise. This high capacity loss is due to the "entropy amplification property"(EAP) of noise with an aperiodic probability distribution. Using the EAP and the duality between WDP and Wyner-Ziv source coding, we also give an example of dramatic rate-loss in quantizing encrypted source.

AB - Costa's "writing on dirty paper"(WDP) shows that the power-constrained channel Y = X + S + Z, with Gaussian Z, has the same capacity as the standard AWGN channel Y = X + Z, provided that the "interference" S (no matter how strong it is) is known at the transmitter. While this ability for perfect interference cancelation is very appealing, it relies heavily on the Gaussianity of the (unknown) noise Z. We construct an example of "bad"noise for writing on dirty paper, namely, "difference set noise". If the interference S is strong, then difference-set noise limits the WDP capacity to at most 2 bits. At the same time, like in the AWGN case, the zero-interference capacity grows without bound with the input constraint. Thus almost 100% of the available capacity is lost in WDP in the presence of difference-set noise. This high capacity loss is due to the "entropy amplification property"(EAP) of noise with an aperiodic probability distribution. Using the EAP and the duality between WDP and Wyner-Ziv source coding, we also give an example of dramatic rate-loss in quantizing encrypted source.

KW - Difference sets

KW - Side information

KW - Writing on dirty paper (WDP)

KW - Wyner-Ziv seup

UR - http://www.scopus.com/inward/record.url?scp=41949137509&partnerID=8YFLogxK

U2 - 10.1109/TIT.2008.917675

DO - 10.1109/TIT.2008.917675

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AN - SCOPUS:41949137509

SN - 0018-9448

VL - 54

SP - 1477

EP - 1487

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 4

ER -