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In space-time shift keying (STSK), the information is conveyed by both the spatial and time dimensions, which can be used to strike a tradeoff between the diversity and multiplexing gains. On the other hand, orthogonal frequency-division multiplexing (OFDM) relying on index modulation (IM) conveys information not only by the conventional signal constellations as in classical OFDM, but also by the indices of the subcarriers. In this paper, we combine the benefits of STSK and IM in order to strike a flexible tradeoff between the throughput and bit-error performance by transmitting extra information bits in each subcarrier block, while increasing the diversity order. In order to further improve this tradeoff, as well as to decrease the complexity of the detector, compressed sensing is combined with the proposed STSK-aided IM system. We first present the maximum likelihood (ML) detection, which forms the best-case bound …