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Existing wireless communication systems have been mainly designed to provide substantial gain in terms of data rates. However, 5G and Beyond will depart from this scheme, with the objective not only to provide services with higher data rates. One of the main goals is to support massive machine-type communications (mMTC) in the IoT applications. Supporting massive uplink (UP) communications for devices with sporadic traffic pattern and short-packet size, as it is in many mMTC use cases, is a challenging task, particularly when the control signaling is not negligible in size compared to the payload. Also, channel estimation is challenging for sporadic and short-packet transmission due to the limited number of employed pilots. In this paper, a new UP multiple access (MA) scheme is proposed for mMTC, which can support a large number of uncoordinated IoT devices with short-packet and sporadic traffic. The proposed UP MA scheme removes the overheads associated with the device identifier as well as pilots related to channel estimation. An alternative mechanism for device identification is proposed, where a unique spreading code is dedicated to each IoT device. This unique code is simultaneously used for the spreading purpose and device identification. Two IoT device identification algorithms which employ sparse signal reconstruction methods are proposed to determine the active IoT devices prior to data detection. Specifically, the BIC model order selection method is employed to develop an IoT device identification algorithm for unknown and time-varying probability of device activity. Our proposed MA scheme benefits from a non-coherent multiuser detection algorithm based on machine learning to enable data detection without a priori knowledge on channel state information. The effectiveness of the proposed MA scheme for known and unknown probability of activity is supported by simulation results.