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1. Quasi-static fading MAC with many users and finite payload

   https://doi.org/10.1109/ISIT.2019.8849781  

   Kowshik, S; Polyanskiy, Y. (July 2019, IEEE Int. Symp. Inf. Theory (ISIT))

   Consider a (multiple-access) wireless communication system where users are connected to a unique base station over a shared-spectrum radio links. Each user has a fixed number k of bits to send to the base station, and his signal gets attenuated by a random channel gain (quasi-static fading). In this paper we consider the many-user asymptotics of Chen-Chen-Guo’2017, where the number of users grows linearly with the blocklength. In addition, we adopt a per-user probability of error criterion of Polyanskiy’2017 (as opposed to classical joint-error probability criterion). Under these two settings we derive bounds on the optimal required energy-perbit for reliable multi-access communication. We confirm the curious behaviour (previously observed for non-fading MAC) of the possibility of perfect multi-user interference cancellation for user densities below a critical threshold. Further we demonstrate the suboptimality of standard solutions such as orthogonalization (i.e., TDMA/FDMA) and treating interference as noise (i.e. pseudo-random CDMA without multi-user detection). 

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2. Low complexity schemes for the random access Gaussian channel

   Ordentlich, Or; Polyanskiy, Yury (June 2017, 2017 IEEE Int. Symp. Inf. Theory (ISIT),)

   We consider an uncoordinated Gaussian multiple access channel with a relatively large number of active users within each block. A low complexity coding scheme is proposed, which is based on a combination of compute-and-forward and coding for a binary adder channel. For a wide regime of parameters of practical interest, the energy-per-bit required by each user in the proposed scheme is significantly smaller than that required by popular solutions such as slotted-ALOHA and treating interference as noise. 

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3. Improved bounds on Gaussian MAC and sparse regression via Gaussian inequalities

   https://doi.org/10.1109/ISIT.2019.8849764  

   Zadik, I.; Polyanskiy, Y.; Thrampoulidis, C. (July 2019, IEEE Int. Symp. Inf. Theory (ISIT))

   We consider the Gaussian multiple-access channel with two critical departures from the classical asymptotics: a) number of users proportional to blocklength and b) each user sends a fixed number of data bits. We provide improved bounds on the tradeoff between the user density and the energy-per-bit. Interestingly, in this information-theoretic problem we rely on Gordon’s lemma from Gaussian process theory. From the engineering standpoint, we discover a surprising new effect: good coded-access schemes can achieve perfect multi-user interference cancellation at low user density. In addition, by a similar method we analyze the limits of false-discovery in binary sparse regression problem in the asymptotic regime of number of measurements going to infinity at fixed ratios with problem dimension, sparsity and noise level. Our rigorous bound matches the formal replica-method prediction for some range of parameters with imperceptible numerical precision. 

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4. On energy-delay tradeoff in uncoordinated MAC

   Yuming Han, Zixiang Xiong (October 2023, Proc. 2023 Allterton conference)

   Polyanskiy [1] proposed a framework for the MAC problem with a large number of users, where users employ a common codebook in the finite blocklength regime. In this work, we extend [1] to the case when the number of active users is random and there is also a delay constraint. We first define a random-access channel and derive the general converse bound. Our bound captures the basic tradeoff between the required energy and the delay constraint. Then we propose an achievable bound for block transmission. In this case, all packets are transmitted in the second half of the block to avoid interference. We then study treating interference as noise (TIN) with both single user and multiple users. Last, we derive an achievable bound for the packet splitting model, which allows users to split each packet into two parts with different blocklengths. Our numerical results indicate that, when the delay is large, TIN is effective; on the other hand, packet splitting outperforms as the delay decreases. 

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5. A Wringing-Based Proof of a Second-Order Converse for the Multiple-Access Channel under Maximal Error Probability

   https://doi.org/10.1109/ISIT45174.2021.9518136  

   Wei, Fei; Kosut, Oliver (July 2021, 2021 IEEE International Symposium on Information Theory (ISIT))

   null (Ed.)

   The second-order converse bound of multiple access channels is an intriguing problem in information theory. In this work, in the setting of the two-user discrete memoryless multiple access channel (DM-MAC) under the maximal error probability criterion, we investigate the gap between the best achievable rates and the asymptotic capacity region. With “wringing techniques” and meta-converse arguments, we show that gap at blocklength n is upper bounded by O(1/√n) . 

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