We propose a new class of space-time block codes based on finite-fieldrank-metric codes in combination with a rank-metric-preserving mapping to theset of Eisenstein integers. It is shown that these codes achieve maximumdiversity order and improve upon certain existing constructions. Moreover, wepresent a new decoding algorithm for these codes which utilizes the algebraicstructure of the underlying finite-field rank-metric codes and employslattice-reduction-aided equalization. This decoder does not achieve the sameperformance as the classical maximum-likelihood decoding methods, but haspolynomial complexity in the matrix dimension, making it usable for large fieldsizes and numbers of antennas.
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