<p>In this paper, an IRS-assisted multi-user massive MIMO system has been designed to increase the transmission rate of the communication. A small number of the elements of the IRS are selected to be active at each time interval. The position of the active IRS elements convey a passive information to the receivers. In order to recover the passive information in the receiver side, the sparse recovery technique has been exploited due to the sparsity property of the support of the phase shift vector. Moreover, the explicit information is transmitted to the receivers using the MIMO beamforming and combining techniques. The beamformer matrix at the transmitter side as well as the combiners at the receivers and the phase shifts of the IRS elements are optimized to attain the maximum transmission rate. The proposed method has been tested in various simulation scenarios. The results indicate that the designed system offers acceptable performance in diverse tests.</p>