TY - JOUR

T1 - Lattice strategies for the dirty multiple access channel

AU - Philosof, Tal

AU - Zamir, Ram

AU - Erez, Uri

AU - Khisti, Ashish J.

N1 - Funding Information:
Dr. Khisti received the NSERC postgraduate fellowship, HP/MIT Alliance Fellowship, the Harold H. Hazen Teaching Award, and the Morris Joseph Levin Masterworks Award.
Funding Information:
Manuscript received April 10, 2009; revised September 11, 2010; accepted January 03, 2011. Date of current version July 29, 2011 This work was supported in part by the Braun-Roger-Siegl Foundation, by the ISF under Grant 1234/08, by BSF under Grant 2004398 and Grant 2008/455. The material in this paper was presented at the IEEE International Symposium on Information Theory (ISIT), Nice, France, June 2007. T. Philosof, R. Zamir, and U. Erez are with the Department of Electrical Engineering—Systems, Tel Aviv University, Tel Aviv, Israel. A. J. Khisti is with the University of Toronto, Toronto, ON, Canada M5S3G4 (e-mail: [email protected]). Communicated by H. Yamamoto, Associate Editor for Shannon Theory. Color versions of one or more figures in this paper are available online at http://ieeeexplore.ieee.org Digital Object Identifier 10.1109/TIT.2011.2158883

PY - 2011/8

Y1 - 2011/8

N2 - 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.

AB - 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.

KW - Channel state information

KW - dirty paper coding

KW - interference alignment

KW - interference cancellation

KW - interference concentration

KW - lattice-strategies

KW - multiple-access channels (MAC)

UR - http://www.scopus.com/inward/record.url?scp=79960993405&partnerID=8YFLogxK

U2 - 10.1109/TIT.2011.2158883

DO - 10.1109/TIT.2011.2158883

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AN - SCOPUS:79960993405

SN - 0018-9448

VL - 57

SP - 5006

EP - 5035

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 8

M1 - 5961842

ER -