Computing channel capacity is in general intractable because it is given by the limit of a sequence of optimization problems whose dimensionality grows to infinity. As a result, constant-sized characterizations of feedback or non-feedback capacity are known for only a few classes of channels with memory. This paper introducesposet-causal channels—a new formalism of a communication channel in which channel inputs and outputs are indexed by the elements of a partially ordered set (poset). We develop a novel methodology that allows us to establish a single-letter upper bound on the feedback capacity of a subclass of poset-causal channels whose memory structure exhibits a Markov property and symmetry. The methodology is based on symmetry reduction in optimization. Additionally, we establish connections to the literature on graphical models by providing a sufficient condition for our capacity upper bound to be tight, expressed in terms of the running intersection property. We instantiate our method on two channel models: the Noisy Output is the STate (NOST) channel—for which the bound is tight—and a new two-dimensional extension of it.

We consider a single-hop wireless network with sources transmitting time-sensitive information to the destination over multiple unreliable channels. Packets from each source are generated according to a stochastic process with known statistics and the state of each wireless channel (ON/OFF) varies according to a stochastic process with unknown statistics. The reliability of the wireless channels is to be learned through observation. At every time-slot, the learning algorithm selects a single pair (source, channel) and the selected source attempts to transmit its packet via the selected channel. The probability of a successful transmission to the destination depends on the reliability of the selected channel. The goal of the learning algorithm is to minimize the Age-of-Information (AoI) in the network over T time-slots. To analyze its performance, we introduce the notion of AoI-regret, which is the difference between the expected cumulative AoI of the learning algorithm under consideration and the expected cumulative AoI of a genie algorithm that knows the reliability of the channels a priori. The AoI-regret captures the penalty incurred by having to learn the statistics of the channels over the T time-slots. The results are two-fold: first, we consider learning algorithms that employ well-known solutions to the stochastic multi-armed bandit problem (such as ϵ-Greedy, Upper Confidence Bound, and Thompson Sampling) and show that their AoI-regret scales as Θ(log T); second, we develop a novel learning algorithm and show that it has O(1) regret. To the best of our knowledge, this is the first learning algorithm with bounded AoI-regret.

Bufferless and single-buffer queueing systems have recently been shown to be effective in coping with escalated Age of Information (AoI) figures arising in single-source status update systems with large buffers and FCFS scheduling. In this paper, for the single-source scenario, we propose a numerical algorithm for obtaining the exact distributions of both the AoI and the peak AoI (PAoI) in (i) the bufferless PH/PH/1/1/P(p) queue with probabilistic preemption with preemption probability p, 0 ≤ p ≤ 1, and (ii) the single buffer M/P H/1/2/R(r) queue with probabilistic replacement of the packet in the queue by the new arrival with replacement probability r, 0 ≤ r ≤ 1. The proposed exact models are based on the well-established theory of Markov Fluid Queues (MFQ) and the numerical algorithms are matrix-analytical and they rely on numerically stable and efficient vector-matrix operations. Moreover, the obtained exact distributions are in matrix exponential form, making it amenable to calculate the tail probabilities and the associated moments straightforwardly. Firstly, we validate the accuracy of the proposed method with simulations, and for sume sub-cases, with existing closed-form results. We then comparatively study the AoI performance of the queueing systems of interest under varying traffic parameters.