Lattice Coding Increases Multicast Rates for Gaussian Multiple-Access Networks

B. Nazer and M. Gastpar

Proceedings of 45th Annual Allerton Conference on Commununication, Control and Computation, Monticello, IL, September 2007.

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Abstract

We study the multicasting problem for additive white Gaussian noise (AWGN) networks with both point-to-point and multiple-access links. The recent discovery of network coding has shown that routing is suboptimal for networks of point-to-point channels: messages must be mixed at intermediate nodes. We showed in earlier work that if a network includes multiple-access channels (MACs) then converting these channels into bit pipes with a channel-network separation-based approach is also suboptimal: the MACs should be used to compute functions reliably as part of an overall network code. In this paper, we give a lattice-based coding strategy for reliably computing linear functions over Gaussian MACs. We then give a computable statement of rates achieved by the resulting network code. In many interesting cases, our achieved rates are higher than those accessible to a separation-based scheme. Our results show that structured codes can be used to derive achievable rates for multi-user communication problems that have been outside the reach of standard i.i.d. random coding arguments.

Notes

Reference

B. Nazer and M. Gastpar, Lattice Coding Increases Multicast Rates for Gaussian Multiple-Access Networks. Proceedings of the 45th Annual Allerton Conference on Commununication, Control and Computation, Monticello, IL, September 2007.

BibTeX

@INPROCEEDINGS(bn_mg_allerton07,
   AUTHOR = "B.~Nazer and M.~Gastpar",
   TITLE = " Lattice Coding Increases Multicast Rates for Gaussian Multiple-Access Networks",
   BOOKTITLE = "Proceedings of 45th Annual Allerton Conference on Commununication, Control and Computation",
   MONTH = "September",
   ADDRESS = "Monticello, IL",
   YEAR = "2007")