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We present finite-blocklength achievability bounds for the unsourcedA-channel. In this multiple-access channel, users noiselessly transmitcodewords picked from a common codebook with entries generated from a $q$-aryalphabet. At each channel use, the receiver observes the set of differenttransmitted symbols but not their multiplicity. We show that the A-channelfinds applications in unsourced random-access (URA) and group testing.Leveraging the insights provided by the finite-blocklength bounds and theconnection between URA and non-adaptive group testing through the A-channel, wepropose improved decoding methods for state-of-the-art A-channel codes and weshowcase how A-channel codes provide a new class of structured group testingmatrices. The developed bounds allow to evaluate the achievable errorprobabilities of group testing matrices based on random A-channel codes forarbitrary numbers of tests, items and defectives. We show that such aconstruction asymptotically achieves the optimal number of tests. In addition,every efficiently decodable A-channel code can be used to construct a grouptesting matrix with sub-linear recovery time.

Finite-Blocklength Results for the A-channel: Applications to Unsourced Random Access and Group Testing