Entropy Amplification Property and the Loss for Writing on Dirty Paper
Aaron S. Cohen, Ram Zamir · IEEE Transactions on Information Theory · 2008
Costa's celebrated ldquowriting on dirty paperrdquo (WDP) shows that the power-constrained channelY=X+S+Z, with GaussianZ, has the same capacity as the standard AWGN channelY=X+Z, provided that the ldquointerferencerdquoS(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) noiseZ. We construct an example of ldquobadrdquo noise for writing on dirty paper, namely, ldquodifference set noiserdquo. If the interferenceSis 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 ldquoentropy amplification propertyrdquo (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.