Yavas, Recep Can and Kostina, Victoria and Effros, Michelle (2021) Gaussian Multiple and Random Access Channels: Finite-Blocklength Analysis. IEEE Transactions on Information Theory, 67 (11). pp. 6983-7009. ISSN 0018-9448. doi:10.1109/tit.2021.3111676. https://resolver.caltech.edu/CaltechAUTHORS:20211122-171053652
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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.
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| 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. | |||||||||
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| Subject Keywords: | Gaussian multiple access channel, Gaussian random access channel, third-order asymptotics, finite blocklength, maximum likelihood decoder, dispersion | |||||||||
| Issue or Number: | 11 | |||||||||
| DOI: | 10.1109/tit.2021.3111676 | |||||||||
| Record Number: | CaltechAUTHORS:20211122-171053652 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20211122-171053652 | |||||||||
| Official Citation: | R. C. Yavas, V. Kostina and M. Effros, "Gaussian Multiple and Random Access Channels: Finite-Blocklength Analysis," in IEEE Transactions on Information Theory, vol. 67, no. 11, pp. 6983-7009, Nov. 2021, doi: 10.1109/TIT.2021.3111676 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 111968 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 22 Nov 2021 18:08 | |||||||||
| Last Modified: | 22 Nov 2021 18:08 |
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