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Many-user MAC is an important model for understanding energy efficiency ofmassive random access in 5G and beyond. Introduced in Polyanskiy'2017 for theAWGN channel, subsequent works have provided improved bounds on the asymptoticminimum energy-per-bit required to achieve a target per-user error at a givenuser density and payload, going beyond the AWGN setting. The best knownrigorous bounds use spatially coupled codes along with the optimal AMPalgorithm. But these bounds are infeasible to compute beyond a few (around 10)bits of payload. In this paper, we provide new achievability bounds for themany-user AWGN and quasi-static Rayleigh fading MACs using the spatiallycoupled codebook design along with a scalar AMP algorithm. The obtained boundsare computable even up to 100 bits and outperform the previous ones at thispayload.

Improved bounds for the many-user MAC