Next-generation cellular systems are anticipated to support 100 times higher data rates (ultra-high rate) compared with the fourth generation (4G) of cellular systems. It is, therefore, necessary to develop novel spectrally efficient uplink/downlink techniques. Multiple techniques have been proposed, including the so-called non-orthogonal multiple access (NOMA) technique. However, the spectral efficiency gains achieved by NOMA over OMA techniques have been shown to be modest. Recently, we proposed a spectrally efficient technique for the downlink channel, which involves exploiting similarities among users’ short bit blocks, where we showed that spectral efficiency gains of up to three times that of OMA schemes can be achieved. However, the technique cannot be extended to the uplink scenario because users are not aware of each other’s bit block. To this end, we propose in this paper a spectrally efficient scheme for the uplink channel, where we exploit the similarity between the short bit blocks of the uplink and downlink sequences corresponding to one user. The downlink bit sequences are those received by a user from the base station (BS). It is assumed that the BS keeps track of the bit sequences transmitted on the downlink channel to different users. The uplink and downlink bit sequences, which are assumed to be uncorrelated, are divided into bit blocks of short lengths, and then, the similarity between those blocks is extracted. Once each user determines its similarity index (i.e., the number of similar bit blocks) between its own bit sequence and its respective downlink bit sequence, this information is communicated with the BS, which will, in turn, select the user with the largest similarity index to transmit during that resource block. The same process repeats every resource block where the user with the maximum similarity index is always selected. We propose a simple overhead exchange algorithm that facilitates the exchange of the information on the similarity indexes between the users and the BS, where we assume that this exchange of information is done through a control channel. The performance of the proposed scheme and the overhead exchange algorithm is investigated analytically and by Monte Carlo simulations. Among the parameters that we incorporate into the analysis are the user density, the length of bit blocks used to check the similarity index, and the channel correlation. We show that spectral efficiency gains of approximately two times that of OMA schemes can be achieved.