Gaussian Multiple and Random Access Channels: Finite-Blocklength Analysis

• Published in: IEEE transactions on information theory Vol. 67; no. 11; pp. 6983 - 7009
• Main Authors: Yavas, Recep Can, Kostina, Victoria, Effros, Michelle
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coders; Codes; Decoding; Dispersion; Encoding; finite blocklength; Gaussian channels; Gaussian multiple access channel; Gaussian random access channel; maximum likelihood decoder; Maximum likelihood decoding; Random access; Receivers; third-order asymptotics; Transmitters
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2021.3111676

This paper presents finite-blocklength achievability bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a sphere and a maximum likelihood decoder, the derived MAC bound on each transmitter's rate matches the MolavianJazi-Laneman bound (2015) in its first- and second-order terms, improving the remaining terms to <inline-formula> <tex-math notation="LaTeX">\frac {1}2\frac {\log {n}}{n}+{O} \left ({\frac {1}{n}}\right) </tex-math></inline-formula> bits per channel use. The result<inline-formula> <tex-math notation="LaTeX">\vphantom {\sum ^{R}} </tex-math></inline-formula> then extends to a RAC model in which neither the encoders nor the decoder knows which of <inline-formula> <tex-math notation="LaTeX">{K} </tex-math></inline-formula> possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time <inline-formula> <tex-math notation="LaTeX">{n}_{t} </tex-math></inline-formula> that depends on the decoder's estimate <inline-formula> <tex-math notation="LaTeX">{t} </tex-math></inline-formula> of the number of active transmitters <inline-formula> <tex-math notation="LaTeX">{k} </tex-math></inline-formula>. Single-bit feedback from the decoder to all encoders at each potential decoding time <inline-formula> <tex-math notation="LaTeX">{n}_{i} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">{i} \leq {t} </tex-math></inline-formula>, informs the encoders when to stop transmitting. For this RAC model, the proposed code achieves the same first-, second-, and third-order performance as the best known result for the Gaussian MAC in operation.