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This article introduces a novel paradigm for the unsourced multiple-accesscommunication problem. This divide-and-conquer approach leverages recentadvances in compressive sensing and forward error correction to produce acomputationally efficient algorithm. Within the proposed framework, everyactive device first partitions its data into several sub-blocks, andsubsequently adds redundancy using a systematic linear block code. Compressivesensing techniques are then employed to recover sub-blocks, and the originalmessages are obtained by connecting pieces together using a low-complexitytree-based algorithm. Numerical results suggest that the proposed schemeoutperforms other existing practical coding schemes. Measured performance liesapproximately $4.3$~dB away from the Polyanskiy achievability limit, which isobtained in the absence of complexity constraints.

A Coupled Compressive Sensing Scheme for Unsourced Multiple Access