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

Abstract

We present finite-blocklength achievability bounds for the unsourced A-channel. In this multiple-access channel, users noiselessly transmit codewords picked from a common codebook with entries generated from a q-ary alphabet. At each channel use, the receiver observes the set of different transmitted symbols but not their multiplicity. We show that the A-channel finds applications in unsourced random-access (URA) and group testing. Leveraging the insights provided by the finite-blocklength bounds and the connection between URA and non-adaptive group testing through the A-channel, we propose improved decoding methods for state-of-the-art A-channel codes and we showcase how A-channel codes provide a new class of structured group testing matrices. The developed bounds allow to evaluate the achievable error probabilities of group testing matrices based on random A-channel codes for arbitrary numbers of tests, items and defectives. We show that such a construction asymptotically achieves the optimal number of tests. In addition, every efficiently decodable A-channel code can be used to construct a group testing matrix with sub-linear recovery time.

Iterative List Patterned Reed-Muller Projection Detection-Based Packetized Unsourced Massive Random Access

“…The main schemes are T -fold irregular repetition (which includes the T -fold irregular repetition slotted ALOHA protocol with collision detection [ 15 , 16 ]), the sparse interleave division multiple access (IDMA) scheme [ 17 ], random spreading and correlation-based energy detection [ 18 , 19 ], as well as the coded compressed sensing (CCS)-based URA scheme [ 20 ]. Coded compressed sensing is a divide-and-conquer strategy that concatenates the inner codes to outer A-channel codes, where a tree code is a specific instance of an outer A-channel code devised for this kind of application [ 21 , 22 ]. This makes it simple to accommodate novel channel models owing to the concatenated form’s adaptability to URA.…”