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Motivated by the demand of cheap hardware and low computational complexity in massive connectivity, we propose a scheme in which transmitters send data encoded by Bloom filter with On-Off Keying (OOK) modulation and receiver performs hard-decision envelope detection on received signals. For frequency-flat fading scenarios with inter-user synchronization (IUS), we develop a Noisy-Combinatorial Orthogonal Matching Pursuit (NCOMP) decoding strategy, and for frequency-selective fading scenarios with IUS, we propose an improved decoding strategy, called multipath-NCOMP (MNCOMP). In addition, we propose a sliding window method to adapt the two decoding strategies to scenarios without IUS. Based on a many-access channel (MnAC) model, we study the asymptotic performance of the proposed scheme for activity recognition and message transmission tasks. Theoretical analysis guarantees that the error probability of our scheme vanishes asymptotically with the number of users, and also shows that the MNCOMP strategy is superior to the NCOMP strategy in frequency-selective fading MnACs. In addition, the proposed sliding window method can ensure that our scheme is immune to the lack of IUS. Numerical experiments corroborate our asymptotic analytical results, for finite number of users.

Massive Access Made Simple: Bloom Filter Based Coding under Hard-decision Envelope Detection