Title :
Optimality of linear codes over PAM for the modulo-additive Gaussian channel
Author :
Hitron, Ayal ; Erez, Uri
Author_Institution :
Dept. of EE-Syst., TAU, Tel Aviv, Israel
Abstract :
It has long been known that linear codes achieve the capacity of additive channels over finite fields. Much less has been known about the performance of linear codes over Zm, when used for communication over channels that are additive with respect to this group. Further, linear codes over Zm play an important role in construction of lattices in Euclidean space. When a construction-A lattice is used for communication over an additive white Gaussian noise channel, a modulo-MZ additive channel with unimodal noise is induced at the receiver. In this paper it is shown that linear codes over Zm achieve the capacity of such channels when the cardinality of the alphabet is a power of a prime.
Keywords :
AWGN channels; binary codes; linear codes; Euclidean space; PAM; additive channels capacity; additive white Gaussian noise channel; binary linear codes; construction-A lattice; finite fields; lattices construction; linear codes optimality; modulo-MZ additive channel; modulo-additive Gaussian channel; unimodal noise; Channel capacity; Lattices; Linear code; Phase shift keying; Signal to noise ratio; Vectors;
Conference_Titel :
Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
978-1-4673-2580-6
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2012.6283576