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Abstract: In a recent work, Coronel et al. initiated the study of the relation betweenthe diversity-multiplexing tradeoff DMT performance of a multiusermultiple-input multiple-output MU-MIMO lattice code and the rate of the decayof the determinants of the code matrix as a function of the size of the signalconstellation. In this note, we state a simple general upper bound on the decayfunction and study the promising code proposed by Badr and Belfiore in closedetail. We derive a lower bound to its decay function based on a classicaltheorem due to Liouville. The resulting bound is applicable also to other codeswith constructions based on algebraic number theory. Further, we study anexample sequence of small determinants within the Badr-Belfiore code and derivea tighter upper bound to its decay function. The upper bound has certainconjectural asymptotic uncertainties, whence we also list the exact bound forseveral finite data rates.



Autor: Jyrki Lahtonen, Roope Vehkalahti, Hsiao-feng Lu, Camilla Hollanti, Emanuele Viterbo

Fuente: https://arxiv.org/







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