Space-time codes based on rank-metric codes and their decoding

In this paper, a new class of space-time block codes is proposed. The new construction is based on finite-field rank-metric codes in combination with a rank-metric-preserving mapping to the set of Eisenstein integers. It is shown that these codes achieve maximum diversity order and improve upon existing constructions. Moreover, a new decoding algorithm for these codes is presented, utilizing the algebraic structure of the underlying finite-field rank-metric codes and employing lattice-reduction-aided equalization. This decoder does not achieve the same performance as the classical maximum-likelihood decoding methods, but has polynomial complexity in the matrix dimension, making it usable for large field sizes and numbers of antennas.