TY - GEN
T1 - Optimality of linear codes over PAM for the modulo-additive Gaussian channel
AU - Hitron, Ayal
AU - Erez, Uri
PY - 2012
Y1 - 2012
N2 - 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 ℤ M, when used for communication over channels that are additive with respect to this group. Further, linear codes over ℤ M 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 ℤ M achieve the capacity of such channels when the cardinality of the alphabet is a power of a prime.
AB - 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 ℤ M, when used for communication over channels that are additive with respect to this group. Further, linear codes over ℤ M 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 ℤ M achieve the capacity of such channels when the cardinality of the alphabet is a power of a prime.
UR - http://www.scopus.com/inward/record.url?scp=84867548768&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2012.6283576
DO - 10.1109/ISIT.2012.6283576
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AN - SCOPUS:84867548768
SN - 9781467325790
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1742
EP - 1746
BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Y2 - 1 July 2012 through 6 July 2012
ER -