Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels
IEEE Transactions on Information Theory
Full-diversity, high-rate space-time block codes from division algebras
IEEE Transactions on Information Theory
The golden code: a 2×2 full-rate space-time code with nonvanishing determinants
IEEE Transactions on Information Theory
Explicit Space–Time Codes Achieving the Diversity–Multiplexing Gain Tradeoff
IEEE Transactions on Information Theory
Perfect Space–Time Block Codes
IEEE Transactions on Information Theory
The coding gain of real matrix lattices: bounds and existence results
IEEE Transactions on Information Theory
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The design of signal constellations for multi-antenna radio communications naturally leads to the problem of finding lattices of square complex matrices with a fixed minimum squared determinant. Since [5] cyclic division algebras, their orders and related structures have become standard material for researchers seeking to construct good MIMO-lattices. In recent submissions [3], [8] we studied the problem of identifying those cyclic division algebras that have the densest possible maximal orders. That approach was based on the machinery of Hasse invariants from class field theory for classifying the cyclic division algebras. Here we will recap the resulting lower bound from [3], preview the elementary upper bounds from [4] and compare these with some suggested constructions. As the lattices of the shape E8 are known to be the densest (with respect to the usual Euclidean metric) in an 8-dimensional space it is natural to take a closer look at lattices of 2×2 complex matrices of that shape. We derive a much tighter upper bound to the minimum determinant of such lattices using the theory of invariants.