Capacity and lattice strategies for canceling known interference

Uri Erez*, Shlomo Shamai, Ram Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)3820-3833
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - Nov 2005


  • Causal side information (SI)
  • Common randomness
  • Dirty-paper channel
  • Dither
  • Interference
  • Minimum mean-squared error (MMSE) estimation
  • Noncausal SI
  • Precoding
  • Randomized code


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