Abstract
In this paper, we focus on the design of unitary space-time codes achieving full diversity using division algebras, and on the systematic computation of their minimum determinant.We also give examples of such codes with high minimum determinant. Division algebras allow to obtain higher rates than known constructions based on finite groups.
Highlights
The problem addressed in the design of space-time codes in the coherent case can be summarized as follows: find a set C of complex n × n matrices such that the minimum determinant δmin(C) = inf | det(X − X )|2
D× may be identified to a subgroup of GLn(C), and taking C to be a subset of D yields a fully diverse algebraic space-time code
The optimality of algebraic codes obtained by Oggier et al on cyclic algebras or crossed product algebras has been established ([2]; see [14])
Summary
In the non-coherent case, the problem has a different flavour: the minimum determinant still needs to be maximized, but the elements of the code C must be complex unitary matrices [3, 4]. We will give a method to construct unitary codes using division algebras carrying a unitary involution, generalizing in particular the work done by Oggier and Lequeu, and how to compute the minimum determinant of such codes. The advantage of this approach compared to the group-theoretic approach is that division algebras allow to obtain higher rates (the rate corresponds, roughly speaking, to the cardinality of the code).
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