Title :
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
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.855591
