Many-broadcast channels: Definition and capacity in the degraded case

Abstract

Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. Motivated by emerging systems with a massive number of users, this paper studies the new many-user paradigm, where the number of users is allowed to grow with the blocklength. The focus of this paper is the degraded many-broadcast channel model, whose number of users may grow as fast as linearly with the blocklength. A notion of capacity in terms of message length is defined and an example of Gaussian degraded many-broadcast channel is studied. In addition, a numerical example for the Gaussian degraded many-broadcast channel with fixed transmit power constraint is solved, where every user achieves strictly positive message length asymptotically.

Many-access channels: The Gaussian case with random user activities

“…The proposed MnAC model together with the capacity result and the compressed sensing based detection technique will provide insights for the optimal design in emerging applications such as machine-tomachine communication, where the number of devices in a cell may far exceed the blocklength. The results also complement a related study of many-broadcast models in [10].…”

Capacity of Gaussian Many-Access Channels

“…Definition 4 (Minimum user identification cost): We say the identification is erroneous in case of any miss or false alarm. For the channel described by (17), the minimum user identification cost is said to be n(ℓ) if n(ℓ) > 0 and for every 0 < ǫ < 1, there exists a signature code of length n 0 = (1 + ǫ)n(ℓ) such that the probability of erroneous identification vanishes as ℓ → ∞, whereas the error probability is strictly bounded away from zero if n 0 = (1 − ǫ)n(ℓ).…”

“…Specifically, joint typicality requires the simultaneous convergence of the empirical joint entropy of every subset of the input and output random variables to the corresponding joint entropy. Even though convergence holds for every subset due to the law of large numbers, the asymptotic equipartition property is not guaranteed because the number of those subsets increases exponentially with the number of users [17]. Resorting to strong typicality does not resolve this because the empirical distribution over an increasing alphabet (due to increasing number of users) does not converge.…”

Physical-Layer Security in the Internet of Things: Sensing and Communication Confidentiality Under Resource Constraints

“…The same need arises for a multipoint-to-point system with a very large number of uplink transmitters. The information-theoretic concepts of [91] and [92] can be a starting point in this direction. In their work, a new paradigm in multiuser information theory models is considered where the number of users can grow arbitrarily large together with the coding blocklength, which is referred to as the many-user regime.…”

“…As a simple example, for a large number of users, the classical capacity/user/channel use tends toward zero, even though the total amount of transmitted information can be arbitrarily large. In the exploratory work of [91] and [92], initial results such as the array of achievable message lengths that can be reliably decoded in the large-user regime (as opposed to channel coding rate) have been presented. Extending these ideas to secret message lengths in the many-user regime would be a worthwhile first step toward a sound theory of physicallayer security in large MTC networks.…”