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This paper considers space-time coding over several independently Rayleighfaded blocks. In particular we will concentrate on giving upper bounds for thecoding gain of lattice space-time codes as the number of blocks grow. Thisproblem was previously considered in the single antenna case by Bayer et al. in2006. Crucial to their work was Odlyzko's bound on the discriminant of analgebraic number field, as this provides an upper bound for the normalizedcoding gain of number field codes. In the MIMO context natural codes areconstructed from division algebras defined over number fields and the codinggain is measured by the discriminant of the corresponding (non-commutative)algebra. In this paper we will develop analogues of the Odlyzko bounds in thiscontext and show how these bounds limit the normalized coding gain of a verygeneral family of division algebra based space-time codes. These bounds canalso be used as benchmarks in practical code design and as tools to analyzeasymptotic bounds of performance as the number of independently faded blocksincreases.

A non-commutative analogue of the Odlyzko bounds and bounds on performance for space-time lattice codes