Lattice strategies for the dirty multiple access channel

Tal Philosof*, Ram Zamir, Uri Erez, Ashish J. Khisti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


In Costa's dirty-paper channel, Gaussian random binning is able to eliminate the effect of interference which is known at the transmitter, and thus achieve capacity. We examine a generalization of the dirty-paper problem to a multiple access channel (MAC) setup, where structured (lattice-based) binning seems to be necessary to achieve capacity. In the dirty-MAC, two additive interference signals are present, one known to each transmitter but none to the receiver. The achievable rates using Costa's Gaussian binning vanish if both interference signals are strong. In contrast, it is shown that lattice-strategies (lattice precoding) can achieve positive rates, independent of the interference power. Furthermore, in some cases-which depend on the noise variance and power constraints-high-dimensional lattice strategies are in fact optimal. In particular, they are optimal in the limit of high SNRwhere the capacity region of the dirty MAC with strong interference approaches that of a clean MAC whose power is governed by the minimum of the users' powers rather than their sum. The rate gap at high SNR between lattice-strategies and optimum (rather than Gaussian) random binning is conjectured to be 1/2 log 2(πe/6)≈0.254 bit. Thus, the doubly dirty MAC is another instance of a network setting, like the Krner-Marton problem, where (linear) structured coding is potentially better than random binning.

Original languageEnglish
Article number5961842
Pages (from-to)5006-5035
Number of pages30
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2011


FundersFunder number
Braun-Roger-Siegl Foundation
Morris Joseph Levin Masterworks Award
Natural Sciences and Engineering Research Council of Canada
United States-Israel Binational Science Foundation2008/455, 2004398
Israel Science Foundation1234/08


    • Channel state information
    • dirty paper coding
    • interference alignment
    • interference cancellation
    • interference concentration
    • lattice-strategies
    • multiple-access channels (MAC)


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