%0 Journal Article %1 yavas2020gaussian %A Yavas, Recep Can %A Kostina, Victoria %A Effros, Michelle %D 2020 %K asymptotics bounds readings %T Gaussian Multiple and Random Access in the Finite Blocklength Regime %U http://arxiv.org/abs/2001.03867 %X 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 $12nn+O(\frac1n)$ 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.

@article{yavas2020gaussian, 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 $\frac{1}{2}\frac{\log n}{n}+O(\frac1n)$ 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 $n_i$, $i \leq t$, 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.}, added-at = {2020-05-23T11:42:04.000+0200}, author = {Yavas, Recep Can and Kostina, Victoria and Effros, Michelle}, biburl = {https://www.bibsonomy.org/bibtex/29f7e70e2f095e4a69e5706207f245769/kirk86}, description = {[2001.03867] Gaussian Multiple and Random Access in the Finite Blocklength Regime}, interhash = {fadf348fce2644edc0fcb5a99d5e3099}, intrahash = {9f7e70e2f095e4a69e5706207f245769}, keywords = {asymptotics bounds readings}, note = {cite arxiv:2001.03867Comment: 25 pages, 1 figure}, timestamp = {2020-05-23T11:42:04.000+0200}, title = {Gaussian Multiple and Random Access in the Finite Blocklength Regime}, url = {http://arxiv.org/abs/2001.03867}, year = 2020 }