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Massive machine-type communications (mMTC) are poised to provide ubiquitous connectivity for billions of Internet-of-Things (IoT) devices. However, the required low-latency massive access necessitates a paradigm shift in the design of random access schemes, which invokes a need of efficient joint activity and data detection (JADD) algorithms. By exploiting the feature of sporadic traffic in massive access, a beacon-aided slotted grant-free massive access solution is proposed. Specifically, we spread the uplink access signals in multiple subcarriers with pre-equalization processing and formulate the JADD as a multiple measurement vector (MMV) compressive sensing problem. Moreover, to leverage the structured sparsity of uplink massive access signals among multiple time slots, we develop two computationally efficient detection algorithms, which are termed as orthogonal approximate message passing (OAMP)-MMV algorithm with simplified structure learning (SSL) and accurate structure learning (ASL). To achieve accurate detection, the expectation maximization algorithm is exploited for learning the sparsity ratio and the noise variance. To further improve the detection performance, channel coding is applied and successive interference cancellation (SIC)-based OAMP-MMV-SSL and OAMP-MMV-ASL algorithms are developed, where the likelihood ratio obtained in the soft-decision can be exploited for refining the activity identification. Finally, the state evolution of the proposed OAMP-MMV-SSL and OAMP-MMV-ASL algorithms is derived to predict the performance theoretically. Simulation results verify that the proposed solutions outperform various state-of-the-art baseline schemes, enabling low-latency random access and high-reliable massive IoT connectivity with overloading.