Real-time monitoring has received considerable attention recently due to its potential in automatic driving, tele-surgery, and factory automation in the 6G era. In remote estimation or reconstruction of stochastic processes, the statistical properties of stochastic processes to be monitored play a central role. Among the stochastic processes interested by real-time applications, the Brownian motion, also known as the Wiener processes is a typical one. In this paper, we are interested in how to monitor Brownian motions efficiently, timely, and reliably. To achieve this goal, we reveal that the real-time estimation error is jointly determined by the quantization error and freshness of data samples. Based on this observation, we present an optimal joint sampling and quantization scheme that efficiently balances the quantization distortion and the age-of-information (AoI). Furthermore, we find that the error accumulation will lead to infinite distortion as monitoring time increases. To overcome this, a multi-layer error correction method is presented for infinite-time monitoring, in which bounded distortion can be achieved with limited data rate. Finally, to conquer the accumulation of transmission errors in unreliable channels, we present an error correction mechanism based on periodic feedback. Diffusion approximation is then adopted to determine the optimal feedback rate and interval.

Real-time monitoring and remote control of stochastic systems have attracted considerable attention due to their potential in task-oriented communications and industrial Internet of Things (IIoT). How to achieve ultra high-freshness in real-time monitoring and remote control becomes a challenging problem. In this paper, we are interested in the freshness oriented source coding with incremental decoding. This is contrast to con-ventional source encoding/decoding, in which a random sample is estimated after its entire codeword is received. Incremental decoding, however, allows the real-time estimation of a random sample once a new bit or channel coding block is decoded in the physical layer. Its source codebook is then optimized, based on which we further conceive a real-time decision policy. Our policies minimize the average mean square error (MSE) or decision cost by judiciously designed codebook for source encoding. Numerical results show that the incremental decoding substantially reduces the MSE and decision cost in real-time monitoring.

Real-time status updating or monitoring plays a critical role in emerging applications including Industrial Internet of Things (IIoT) and Vehicular-to-Everything (V2X) systems. In these applications, the real-time status is mostly characterized by analog signal samples desiring lossy compression before digital transmissions. However, how to ensure the data freshness while reducing the distortion due to lossy compression still remains open. In this paper, we are interested in a cross-layer framework aiming at achieving low Age-of-Information (AoI) and compression distortion concurrently in real-time monitoring over fading channels. More specifically, a cross-layer optimization is formulated to jointly control the lossy compression in the application layer and data transmission in the physical layer. We present a hierarchical solution method by decomposing the cross-layer optimization into inner and outer problems. The objective of the inner problem, solved by convex optimization, is to minimize an age-weighted distortion function and strike the optimal tradeoff between the instantaneous AoI and compression loss. The objective of the outer problem, solved by dimension-reduced Constrained Markov Decision Process (CMDP), is to acquire the optimal scheduling policy reducing the average AoI and distortion. We demonstrate the structural results of the optimal cross-layer design, which substantially reduces the protocol complexity in practice.

Low-latency communication is expected to play a key role in the Industrial Internet of Things (IIoT). Although there has been considerable effort on reducing latency, few attention has been focused on the low-latency transmission of distortion-tolerant data, e.g. IIoT's analog samples, over fading channels. In this paper, we present a cross-layer approach to jointly adapt the transmission power, rate, and compression ratio based on the instantaneous buffer and channel states. In particular, to minimize the average delay under both average power and distortion constraints, we formulate a Constrained Markov Decision Process (CMDP) with multi-dimensional state and action spaces. A novel solution is then presented by judiciously decomposing the multi-dimensional CMDP into a deterministic hierarchical optimization consisting of a linear programming and a convex optimization problem. Furthermore, we show the optimality of a threshold-based scheduling policy that highly reduces the complexity and present an optimal delay-power-distortion tradeoff that characterizes a fundamental performance tradeoff between the physical, network, and application layers. The joint lossy compression and power allocation scheme realizes a deep cross-layer optimization of source coding, queuing control, and wireless transmission, which outperforms the traditional cross-layer design consisting of only two layers, not to mention layered protocols.

Most recently, Ultra-Reliable Low-Latency Communication (URLLC) has attracted much attention due to its potential application in Factory Automation (FA), Vehicle-to-everything (V2X), telesurgery, etc. One of the key performance metrics for URLLC is the Queue-Length-Bound (QLB) violation probability. However, how to minimize the QLB violation probability remains open over time-varying channels because it relies on challenging cross-layer designs. In this paper, we formulate a Constrained Markov Decision Process (CMDP) framework to minimize this QLB violation probability while keeping the average transmission power low. To achieve a feasible solution, we then relax this CMDP problem into an unconstrained Markov Decision Process (MDP) and apply the value iteration algorithm. By this means, we acquire the optimal stationary deterministic policy. It is further shown that a threshold based policy can strike the optimal QLB violation probability and power tradeoff. Finally, a Linear Programming (LP) is adopted to solve this CMDP given a certain power constraint. We thus acquire the optimal probabilistic policy and its tradeoff between the QLB violation probability and the transmission power.

Delay-sensitive communication has attracted much recent attention in emerging 5G systems that are expected to provide Ultra-Reliable Low-Latency Communications (URLLC). However, it remains open on how to balance the queuing delay and the compression distortion in power-constrained transmission over time-varying channels. In this paper, we present a cross-layer approach to strike the optimal delay-power-distortion tradeoff. More specifically, the compression ratio in the application layer and the data rate in the physical layer jointly adapt to the buffer and channel state. To this end, we formulate a nonlinear optimization problem with a constrained Markov Decision Process (CMDP) to minimize the average queuing delay while keeping the distortion and power consumption low. Converting this problem into Linear Programming (LP) gives us both the optimal scheduling parameters and its delay-power-distortion tradeoff. We next show that the tradeoff between delay, power, and distortion could be further improved by introducing the weighted-average cost of power and distortion for each action. The weighted-average costs can be minimized and optimized to be a convex function of the transmission rate. With this convex cost-rate function, we find the optimal threshold-based policy.

Successive relaying holds the promise of recovering the multiplexing loss due to the half-duplex constraint, by allowing the source and relays to transmit messages simultaneously, but it may cause severe inter-relay interference (IRI). To overcome this, we apply an amplify-and-cancel method proposed in our previous work by Chen et al. into the successive amplify-and-forward (AF) relay model, thereby conceiving successive AF relaying with network interference cancellation. The proposed protocol benefits from low complexity because IRI is mitigated by linear analog processing without decoding any inter-relay signals. More specifically, a relay keeps receiving signals from the source and other relays before its own transmission, in order to obtain the prior knowledge of IRI that can be used to mitigate the IRI. We present an iterative expression of the power of the residual interference, based on which the achievable rate and the outage probability of the proposed scheme are derived. We further minimize its outage probability by optimizing the order of relays and present the optimal diversity and multiplexing tradeoff.