Lattices which are good for (almost) everything

Uri Erez; Simon Litsyn; Ram Zamir

doi:10.1109/TIT.2005.855591

Lattices which are good for (almost) everything

Uri Erez^*, Simon Litsyn, Ram Zamir

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3401-3416
Number of pages	16
Journal	IEEE Transactions on Information Theory
Volume	51
Issue number	10
DOIs	https://doi.org/10.1109/TIT.2005.855591
State	Published - Oct 2005

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

Access to Document

10.1109/TIT.2005.855591

Cite this

@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",

}

TY - JOUR

T1 - Lattices which are good for (almost) everything

AU - Erez, Uri

AU - Litsyn, Simon

AU - Zamir, Ram

N1 - 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.

PY - 2005/10

Y1 - 2005/10

N2 - 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.

AB - 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.

KW - Coding for unconstrained additive white Gaussian noise (AWGN) channel

KW - Lattice codes

KW - Loeliger ensemble

KW - Meansquared error (MSE) quantization

KW - Minkowski bound

KW - Poltyrev exponent

KW - Sphere covering

KW - Sphere packing

UR - http://www.scopus.com/inward/record.url?scp=26844546304&partnerID=8YFLogxK

U2 - 10.1109/TIT.2005.855591

DO - 10.1109/TIT.2005.855591

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:26844546304

SN - 0018-9448

VL - 51

SP - 3401

EP - 3416

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 10

ER -

Lattices which are good for (almost) everything

Abstract

Keywords

Access to Document

Other files and links

Cite this