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Capacity and lattice strategies for canceling known interference

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3 Author(s)
Erez, U. ; Dept. of Electr. Eng.-Syst., Tel-Aviv Univ., Israel ; Shamai, S. ; Zamir, R.

We consider the generalized dirty-paper channel Y=X+S+N,E{X2}≤PX, where N is not necessarily Gaussian, and the interference S is known causally or noncausally to the transmitter. We derive worst case capacity formulas and strategies for "strong" or arbitrarily varying interference. In the causal side information (SI) case, we develop a capacity formula based on minimum noise entropy strategies. We then show that strategies associated with entropy-constrained quantizers provide lower and upper bounds on the capacity. At high signal-to-noise ratio (SNR) conditions, i.e., if N is weak relative to the power constraint PX, these bounds coincide, the optimum strategies take the form of scalar lattice quantizers, and the capacity loss due to not having S at the receiver is shown to be exactly the "shaping gain" 1/2log(2πe/12)≈ 0.254 bit. We extend the schemes to obtain achievable rates at any SNR and to noncausal SI, by incorporating minimum mean-squared error (MMSE) scaling, and by using k-dimensional lattices. For Gaussian N, the capacity loss of this scheme is upper-bounded by 1/2log2πeG(Λ), where G(Λ) is the normalized second moment of the lattice. With a proper choice of lattice, the loss goes to zero as the dimension k goes to infinity, in agreement with the results of Costa. These results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels.

Published in:

Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 11 )

Date of Publication:

Nov. 2005

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