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We discuss the problem of designing channel access architectures for enablingfast, low-latency, grant-free and uncoordinated uplink for densely packedwireless nodes. Specifically, we study random-access codes, previouslyintroduced for the AWGN multiple-access channel (MAC) by Polyanskiy'2017, inthe practically more relevant case of users subject to Rayleigh fading, whenchannel gains are unknown to the decoder. We propose a random codingachievability bound, which we analyze both non-asymptotically (at finiteblocklength) and asymptotically. As a candidate practical solution, we proposean explicit sparse-graph based coding scheme together with an alternatingbelief-propagation decoder. The latter's performance is found to besurprisingly close to the finite-blocklength bounds. Our main findings aretwofold. First, just like in the AWGN MAC we see that jointly decoding largenumber of users leads to a surprising phase transition effect, where atspectral efficiencies below a critical threshold (5-15 bps/Hz depending onreliability) a perfect multi-user interference cancellation is possible.Second, while the presence of Rayleigh fading significantly increases theminimal required energy-per-bit $E_b/N_0$ (from about 0-2 dB to about 8-11 dB),the inherent randomization introduced by the channel makes it much easier toattain the optimal performance via iterative schemes.  In all, it is hoped that a principled definition of the random-access modeltogether with our information-theoretic analysis will open the road towardsunified benchmarking and comparison performance of various random-accesssolutions, such as the currently discussed candidates (MUSA, SCMA, RSMA) forthe 5G/6G.

Energy efficient coded random access for the wireless uplink