May  2008, 2(2): 131-145. doi: 10.3934/amc.2008.2.131

The equivalence of space-time codes and codes defined over finite fields and Galois rings

1. 

Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0395

2. 

Department of Electrical and Computer Engineering, University of Colorado at Boulder, Boulder, CO 80309-0425, United States

Received  October 2007 Revised  April 2008 Published  April 2008

Space-time codes for a wide variety of channels have the property that the diversity of a pair of codeword matrices is measured by the vanishing or non-vanishing of polynomials in the entries of the matrices. We show that for every such channel: I) There is an appropriately-defined notion of approximation of space-time codes such that each code is arbitrarily well approximated by one whose alphabet lies in the field of algebraic numbers; II) Each space-time code whose alphabet lies in the field of algebraic numbers is an appropriately-defined lift from a corresponding space-time code defined over a finite field or a ''scaled'' lift from a Galois ring of arbitrary characteristic. This implies that all space-time codes can be designed over finite fields or over Galois rings of arbitrary characteristic and then lifted to complex matrices with entries in a number field.
Citation: David Grant, Mahesh K. Varanasi. The equivalence of space-time codes and codes defined over finite fields and Galois rings. Advances in Mathematics of Communications, 2008, 2 (2) : 131-145. doi: 10.3934/amc.2008.2.131
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