Optimality of linear codes over PAM for the modulo-additive Gaussian channel
Ayal Hitron, Uri Erez · 2012
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 Zmplay 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 Zmachieve the capacity of such channels when the cardinality of the alphabet is a power of a prime.