@article{83a5c661963b41fd81f9b2321a741f6f,
title = "Lattices which are good for (almost) everything",
abstract = "We define an ensemble of lattices, and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings, sphere coverings, additive white Gaussian noise (AWGN) channel codes and mean-squared error (MSE) quantization codes. These lattices are generated by applying Construction A to a random linear code over a prime field of growing size, i.e., by {"}lifting{"} the code to ℝn.",
keywords = "Coding for unconstrained additive white Gaussian noise (AWGN) channel, Lattice codes, Loeliger ensemble, Meansquared error (MSE) quantization, Minkowski bound, Poltyrev exponent, Sphere covering, Sphere packing",
author = "Uri Erez and Simon Litsyn and Ram Zamir",
note = "Funding Information: Manuscript received June 2, 2003; revised June 7, 2005. The work of S. Litsyn was supported in part by the ISF and the Binational Science Foundation under Grant BSF1999-099. The work of R. Zamir was supported in part by the Israel Academy of Science Research Fund under Grant ISF 65-01. The material in this paper was presented in part at the IEEE Information Theory Workshop, Paris, France, April 2003.",
year = "2005",
month = oct,
doi = "10.1109/TIT.2005.855591",
language = "אנגלית",
volume = "51",
pages = "3401--3416",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "10",
}