Publication: Finite-blocklength results for the A-channel: applications to unsourced random access and group testing
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2022-09-27
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IEEE
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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.
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Proceedings of: 58th Annual Allerton Conference on Communication, Control, and Computing, 27-30 September 2022, Monticello, USA.
Keywords
Computer science, Codes, Costs, Error probability, Symbols, Receivers, Encoding
Bibliographic citation
Lancho, A., Fengler, A. & Polyanskiy, Y. (27-30 September 2022). Finite-blocklength results for the A-channel: applications to unsourced random access and group testing [proceedings]. 58th Annual Allerton Conference on Communication, Control, and Computing, Monticello, USA.