A Coupled Compressive Sensing Scheme for Uncoordinated Multiple Access
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This article introduces a novel communication scheme for the uncoordinated multiple-access communication problem. The proposed divide-and-conquer approach leverages recent advances in compressive sensing and forward error correction to produce an uncoordinated access scheme, along with a computationally efficient decoding algorithm. Within this framework, every active device first partitions its data into several sub-blocks and, subsequently, adds redundancy using a systematic linear block code. Compressive sensing techniques are then employed to recover sub-blocks up to a permutation of their order, and the original messages are obtained by connecting pieces together using a low-complexity, tree-based algorithm. Explicit closed form expressions are derived to characterize the error probability and computational complexity of this access paradigm. An optimization framework, which exploits the trade-off between error probability and computational complexity, is developed to assign parity check bits to each sub-block. Specifically, two different parity check bit allocation strategies are discussed and their performances are analyzed in the limit as the number of active users and their corresponding payloads tend to infinity. The number of channel uses needed and the computational complexity associated with these allocation strategies are explicitly characterized for various scaling regimes. In terms of error performance, it is shown that the proposed scheme fails with vanishing probability in the asymptotic setting where the number of active users grows unbounded. Numerical results show that this novel scheme outperforms other existing practical coding strategies. Measured performance lies approximately 4.3 dB away from the Polyanskiy achievability bound, which is derived in the absence of complexity constraints
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