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Published November 2021 | public
Journal Article

Gaussian Multiple and Random Access Channels: Finite-Blocklength Analysis

Abstract

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 ½ log n/n + O(1/n) bits per channel use. The result then extends to a RAC model in which neither the encoders nor the decoder knows which of K possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time n_t that depends on the decoder's estimate t of the number of active transmitters k. Single-bit feedback from the decoder to all encoders at each potential decoding time n_i, I ≤ t , 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.

Additional Information

© 2021 IEEE. Manuscript received June 20, 2020; revised April 22, 2021; accepted August 23, 2021. Date of publication September 10, 2021; date of current version October 20, 2021. This work was supported by the National Science Foundation (NSF) under Grant CCF-1817241. An earlier version of this paper was presented in part at the 2020 International Symposium on Information Theory (ISIT'20) [DOI: 10.1109/ISIT44484.2020.9174026]. The authors are grateful to Peida Tian for pointing out the paper [41] that led to an improvement in Lemma 4.

Additional details

Created:
August 22, 2023
Modified:
October 23, 2023