We investigate opportunities of devising a sparse multi-carrier index keying (MCIK) method for orthogonal frequency division multiplexing (OFDM) system, which uses additionally the sparse carrier indices to transmit the data, and improve the performance of signal detection. In MCIK-OFDM transmission, only a subset of sub-carriers is activated, according to the incoming data, to convey constellation symbols. The use of activated sub-carrier indices as an additional degree of freedom enables the transmission of extra information bits without any additional bandwidth and power requirements. This MCIKOFDM principle aims to improve the reliability and the energy efficiency for energy constrained wireless systems (e.g., M2M, 3GPP’s NB-IoT). Although a receiver of MCIK-OFDM is able to exploit a power gain with precoding in OFDM, the error performance of MCIK-OFDM is not satisfactory with the limited diversity order of one. For example, using a repetition diversity, called as repeated MCIK-OFDM (ReMO), we can enhance the reliability compared to the conventional MCIK-OFDM and OFDM techniques, for a given spectral efficiency. To gain a comprehensive insight into the ReMO performance, a new framework for evaluating the symbol error performance is studied and a simple, closed-form expression for the SEP is provided. Similarly, considering MCIK principles, we can overview various design concepts of MCIK-OFDM which are suitable to future machine type communications.