Abstract-In space-time shift keying (STSK), the information is conveyed by both the spatial and time dimensions, which can be used to strike a trade-off 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 trade-off between the throughput and bit-error performance by transmitting extra information bits in each subcarrier block, whilst increasing the diversity order. In order to further improve this trade-off, as well as to decrease the complexity of the detector, compressed sensing (CS) is combined with the proposed STSK-aided IM system. We first present the Maximum LikeLihood (ML) detection, which forms the best-case bound on the proposed system's performance. Then we propose a pair of reduced-complexity detection algorithms capable of approaching the ML detector's performance. Furthermore, in order to attain a near capacityperformance, we propose a soft-input soft-output (SISO) decoder that is capable of exchanging soft-information with a channel decoder through iterative decoding.