TY - JOUR

T1 - Capacity and lattice strategies for canceling known interference

AU - Erez, Uri

AU - Shamai, Shlomo

AU - Zamir, Ram

N1 - Funding Information:
Manuscript received August 4, 2002; revised October 22, 2004 and July 18, 2005. This work was supported in part by the Israel Academy of Science under Grant 65/01. The material in this paper was presented in part at the Cornell Summer Workshop on Information Theory, Ithaca, NY, August 2000, and at the IEEE International Symposium on Information Theory and Its Applications, Honolulu, HI, November 2000. U. Erez and R. Zamir are with the Department of Electrical Engineering–Systems, Tel-Aviv University, Ramat-Aviv 699978, Tel-Aviv, Israel. S. Shamai (Shitz) is with the Department of Electrical Engineering, Tech-nion–Israel Institute of Technology, Technion City, Haifa 32000, Israel. Communicated by ˙. E. Telatar, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2005.856935

PY - 2005/11

Y1 - 2005/11

N2 - 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" 1/2 log(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 1/2 log 2πeG(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.

AB - 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" 1/2 log(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 1/2 log 2πeG(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.

KW - Causal side information (SI)

KW - Common randomness

KW - Dirty-paper channel

KW - Dither

KW - Interference

KW - Minimum mean-squared error (MMSE) estimation

KW - Noncausal SI

KW - Precoding

KW - Randomized code

UR - http://www.scopus.com/inward/record.url?scp=27744491562&partnerID=8YFLogxK

U2 - 10.1109/TIT.2005.856935

DO - 10.1109/TIT.2005.856935

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AN - SCOPUS:27744491562

SN - 0018-9448

VL - 51

SP - 3820

EP - 3833

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 11

ER -