An elementary condition for non-norm elements

Authors:
Xiaoyong Guo;Xiang-Gen Xia
Affiliations:
Department of Electrical and Computer Engineering, University of Delaware, Newark, DE;Department of Electrical and Computer Engineering, University of Delaware, Newark, DE
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

Cyclic division algebra (CDA) has recently become a major technique to construct space-time block codes with nonvanishing determinant (NVD). One of the key steps in this technique is the determination of non-norm elements and a sufficient condition for the determination has been given by Kiran and Rajan lately based on algebraic number theory. In this paper, based on Kiran and Rajan's condition, we present a more elementary condition for non-norm elements when signals are QAM or HEX, which is easier to check. With this elementary condition, non-norm elements with smaller absolute values than the existing ones can be found.