Lattices which are good for (almost) everything

Author

Erez, Uri ; Litsyn, Simon ; Zamir, Ram

Author_Institution

Dept. of Electr. Eng.-Syst., Tel-Aviv Univ., Israel

Volume

51

Issue

10

fYear

2005

Firstpage

3401

Lastpage

3416

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

AWGN channels; channel coding; linear codes; mean square error methods; random codes; AWGN channel codes; Loeliger ensemble; MSE; Minkowski bound; Poltyrev exponent; additive white Gaussian noise channel; lattice codes; mean-squared error; quantization codes; random linear code; sphere coverings; sphere packings; AWGN; Additive white noise; Channel coding; Error correction codes; Error probability; Information theory; Lattices; Linear code; Maximum likelihood decoding; Quantization; Coding for unconstrained additive white Gauss- ian noise (AWGN) channel; Loeliger ensemble; Minkowski bound; Poltyrev exponent; lattice codes; mean-squared error (MSE) quantization; sphere covering; sphere packing;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2005.855591

Filename

1512416