We consider a base station (BS) that receives version update packets from multiple streams and broadcasts them using non-orthogonal multiple access (NOMA) over a fading broadcast channel. Sequentially indexed packets arrive randomly, rendering previous ones obsolete. The version age of information (VAoI) at a user is defined as the difference between the latest packet’s version index at the BS and at the user. Our objective is to minimize the average VAoI across users, subject to an average power constraint at the BS, by optimally scheduling and transmitting packets with sufficient power for successful delivery. We consider channel-only stationary randomized policies (CO-SRP), making transmission decisions based on channel power gains, and obtain optimal CO-SRP, showing that VAoI achieved with CO-SRP is within twice the optimal VAoI. We also develop a Constrained Markov Decision Process (CMDP)-based solution, several heuristic benchmarks, and analyze CMDP policy properties. Simulations compare achievable VAoI and computational performance of various policies and reveal differences between optimizing AoI and VAoI. Notably, a scheme allowing transmission to at most one user at a time matches NOMA’s performance under strict power constraints but is outperformed when constraints are relaxed. Additionally, AoI-optimized policies result in higher VAoI compared to VAoI-optimized policies and vice versa, when user arrival rates are mismatched.

The problem of packing smaller objects within a larger object has been of interest for decades, including in information and coding theory. In these problems, in addition to the requirement that the smaller objects must lie completely inside the larger objects, they are expected to not overlap or have minimum overlap with each other. Due to this, the problem of packing turns out to be a non-convex problem, obtaining whose optimal solution is challenging. As such, several heuristic approaches have been used for obtaining sub-optimal solutions in general, and provably optimal solutions for some special instances. In this paper, we propose a novel encoder-decoder architecture consisting of an encoder block, a perturbation block and a decoder block, for packing identical circles within a larger circle. In our approach, the encoder takes the index of a circle to be packed as an input and outputs its center through a normalization layer, the perturbation layer adds controlled perturbations to the center, ensuring that it does not deviate beyond the radius of the smaller circle to be packed, and the decoder takes the perturbed center as input and estimates the index of the intended circle for packing. We parameterize the encoder and decoder by a neural network and optimize it to reduce an error between the decoder's estimated index and the actual index of the circle provided as input to the encoder. The proposed approach can be generalized to pack objects of higher dimensions and different shapes by carefully choosing normalization and perturbation layers. The approach gives a sub-optimal solution and is able to pack smaller objects within a larger object with competitive performance with respect to classical methods.

Timely sampling and fresh information delivery are important in 6G communications. This is achieved by encoding samples into short packets/codewords for transmission, with potential decoding errors. We consider a broadcasting base station (BS) that samples information from multiple sources and transmits to respective destinations/users, using short-blocklength cyclic and deep learning (DL) based codes for error correction, and cyclic-redundancy-check (CRC) codes for error detection. We use a metric called reported age of information (AoI), abbreviated as RAoI, to measure the freshness of information, which increases from an initial value if the CRC reports a failure, else is reset. We minimize long-term average expected RAoI, subject to constraints on transmission power and distortion, for which we obtain age-agnostic randomized and age-aware drift-plus-penalty policies that decide which user to transmit to, with what message-word length and transmit power, and derive bounds on their performance. Simulations show that longer CRC codes lead to higher RAoI, but the RAoI achieved is closer to the true, genie-aided AoI. DL-based codes achieve lower RAoI. We conclude that prior AoI optimization literature with finite blocklengths substantially underestimates AoI because they assume all errors can be detected perfectly without using CRC.

Emerging deep learning methods for satellite-derived bathymetry (SDB), in which water depth is estimated using satellite band reflectance values, typically treat the problem as either classification or regression tasks, which can underperform, particularly when the depth data exhibits a skewed distribution. In this work, we propose a novel jointly-trained classification-regression (JTCR) model for SDB that first classifies the input band reflectance values to correspond to a depth range and then performs regression within each range. Using Shetrunji reservoir, an inland reservoir in India, as a case study, with Sentinel-2 band reflectance values, we demonstrate that our proposed model outperforms other competitive deep learning models, including the model derived from the separate training of classification and regression tasks in the proposed classification-regression architecture. Concretely, we observe Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and R-squared (R2) values of 0.17, 0.05, and 0.99, respectively, in the proposed JTCR model, compared to 0.99, 0.71, and 0.85 in the feedforward neural network model.

In the IEEE 802.11ax standard, a mode of operation called target wake time (TWT) is introduced towards enabling deterministic scheduling in WLAN networks. In the TWT mode, a group of stations (STAs) can negotiate with the access point (AP) a periodically repeating time window, referred to as TWT Service Period (TWT-SP), over which they are awake and outside which they sleep for saving power. The offset from a common starting time to the first TWT-SP is referred to as the TWT Offset (TWT-O) and the periodicity of TWT-SP is referred to as the TWT Wake Interval (TWT-WI). In this work, we consider communication between multiple STAs with heterogeneous traffic flows and an AP of an IEEE 802.11ax network operating in the TWT mode. Our objective is to maximize a long-term weighted average timely throughput across the STAs, where the instantaneous timely throughput is defined as the number of packets delivered successfully before their deadlines at a decision instant. To achieve this, we obtain algorithms, composed of (i) an inner resource allocation (RA) routine that allocates resource units (RUs) and transmit powers to STAs, and (ii) an outer grouping routine that assigns STAs to (TWT-SP, TWT-O,TWT-WI) triplets. For inner RA, we propose a near-optimal low-complexity algorithm using the drift-plus-penalty (DPP) framework and we adopt a greedy algorithm as outer grouping routine. Via numerical simulations, we observe that the proposed algorithm, composed of a DPP based RA and a greedy grouping routine, performs better than other competitive algorithms.

We consider a source node deployed in a real-time monitoring application that needs to sample a stochastic process and convey its state timely and accurately to a destination over a wireless ON/OFF channel. The source can either process a raw sample to determine its current state and transmit that information or transmit the raw sample and let the destination determine the state. The source is subjected to an average cost constraint, and it cannot sample, process, and transmit at all the time instants due to the associated costs. When the destination does not receive information, it uses the previous information as an estimate of the current state, which, if it matches the actual state at the source, the distortion is considered to be zero. The objective is to minimize average expected distortion subject to constraints on the average expected age of information (AoI) of states of interest and costs incurred by the source, where the AoI of a state increases if no status update is received, else drops to unity. We derive a stationary randomized policy (SRP) to solve the formulated problem, for which we obtain the expression for the expected AoI under the SRP using a lumpability argument on the two-dimensional discrete-time Markov chain formed using AoI and instantaneous distortion as states. We extensively study the impact of the system parameters on the average distortion under the SRP and draw significant conclusions.

In many real-time applications, timely accessibility to actionable insights is an important requirement. We consider users equipped with sensors and actuators, where the sensors generate updates which need to be processed for driving the actuators. The processing task can be carried out locally or at an edge server located at a common base station (BS). The users access the BS via a fading multiple access channel (MAC) using a non-orthogonal multiple access technique. To measure the timeliness of processed information, we adopt a metric called age of processed information (AoPI), defined as the time elapsed since the generation of the last successfully processed packet available to the user. In this setting, we formulate an average AoPI minimization problem, when users are subjected to average power constraints. The BS has to decide when the users should generate status updates and whether to process them locally or at the edge server. We cast the problem as a constrained Markov decision process (CMDP) and obtain its solution via Lagrangian relaxation. We then obtain a simpler policy via Lyapunov optimization and bound its performance. Via numerical simulations, we finally illustrate properties of the CMDP solution and study behavior of average AoPIs under different policies when problem parameters are varied.

In many real-time applications, timely accessibility to actionable insights, usually obtained by processing raw status updates, is an important requirement. In this paper, we consider users equipped with sensors and actuators. The sensors of a user generate status updates which need to be processed for driving the actuators of the user. The processing task of a user can be carried out locally or it can be offloaded to an edge server, located at a common base station (BS). The users access the BS via a fading multiple access channel using a non-orthogonal multiple access scheme. To measure the timeliness of processed information, we adopt a metric called age of processed information (AoPI), defined as the time elapsed since the generation of last successfully processed packet available at the user. In this setting, we formulate a problem for minimizing a long-term average AoPI across the users, when the users are subjected to average power constraints. The BS has to decide when a user should generate a status update and whether it should be processed locally or at the edge server. We cast the problem as a constrained Markov decision process (CMDP) and solve it via Lagrangian relaxation. We derive several structural properties of the optimal solution to the relaxed problem. We also obtain a simpler policy via Lyapunov optimization and bound its performance. Using numerical simulations, we demonstrate the derived structural properties and compare average AoPIs under different policies.

Many emerging Internet of Things (IoT) sensors deployed for sampling and delivering status update packets may be powered by energy harvesting (EH) sources. In this work, we consider a sensor-monitor pair, where the EH-powered sensor delivers timely updates to the monitor over a fading channel. We deem a status update to be successful if it contains at least$R_{0}$bits. The sensor is equipped with a finite-capacity non-ideal battery whose charging and discharging losses are proportional to charging and discharging powers. The sensor consumes non-negligible circuit power for its operation. Under this setting, we quantify timeliness of information by the age of information (AoI) metric and consider an AoI minimization problem for optimally choosing charging and discharging powers, transmission duration and transmit power at each communication slot. We cast this problem as a Markov decision process (MDP), in which the action tuple can take a wide range of values, and solve it using the value iteration algorithm. We reduce the computational complexity of the value iteration, by showing that the optimal action takes one of the two values, which result in either no transmission or delivery of$R_{0}$bits, and that it has a threshold structure in AoI when all other variables are fixed. Via numerical simulations, we illustrate the threshold structure of the optimal action and compare the performance of the MDP-based policy with other simpler heuristic policies.

Emerging fifth generation and beyond networks are expected to deliver accurate information as fresh as possible. In this work, we consider a wireless fading multiple access channel, where M users communicate to a base station (BS) in a time-slotted system. Each user can sample an information packet in any slot of interest, compress it to a finite number of bits and then transmit the compressed packet to the BS. The compression and transmission result in distortion and power consumption, respectively. Using the age of information (AoI) metric for quantifying freshness of information, we consider minimization of a long-term weighted average AoI across the users, subject to average power and distortion constraints at each user, for obtaining the number of bits to be transmitted by a user in a given slot. We cast the problem as a constrained Markov decision process (CMDP) and solve it via Lagrange relaxation. We show that a threshold-type policy is optimal for the relaxed problem. We also propose a convex optimization problem to obtain a suboptimal but simpler stationary randomized policy, whose minimum achievable average AoI is within twice that of the optimal policy. Via numerical simulations, we illustrate the threshold structure of the CMDP based solution and study variation of the average AoIs achieved by the proposed policies when the bounds on the average power and distortion constraints are varied.

We consider a source that sends freshness-sensitive status updates about an auto-regressive Markov process to a monitor, in a time-slotted system. The source samples the random process at the start of every slot and decides whether to transmit the sample or not. The transmission of a sample incurs a fixed cost. When a monitor receives a sample, its information about the source is perfect. However, when no samples are received, it estimates the realization of the process based on previously received samples. We adopt a metric referred to as the age of incorrect estimates (AoIE), defined as the product of an estimation error, E, and, v, the time elapsed since the latest time at which the monitor had a sufficiently correct estimate. We formulate an optimization problem to decide when a source must transmit a packet for minimizing the long-term average expected weighted sum of the AoIE and the transmission cost. We cast this problem as a Markov decision process and prove that the optimal policy is a threshold-type policy, in which, for a fixed v, there exists a threshold on E beyond which it is optimal to transmit, and vice versa. Using numerical simulations, we illustrate this threshold structure of the optimal policy. We also consider a simple periodic policy in which the information packets are transmitted periodically, after every fixed number of slots, irrespective of the realizations of E and v, and numerically show that its performance is significantly worse than that of the optimal threshold-type policy.

Freshness of information is an important requirement in many real-time applications. It is measured by a metric called the age of information (AoI), defined as the time elapsed since the generation of the last successful update received by the destination. We consider M sources (users) updating their statuses to a base station (BS) over a block-fading multiple access channel (MAC). At the start of each fading block, the BS acquires perfect information about channel power gain realizations of all the users in the block. Using this information, a centralized scheduling policy at the BS decides, for each block, which users should transmit and with what powers. The objective is to minimize a long-term weighted average AoI across all users subject to a long-term average power constraint at each user. Under this setting, we first consider a simple time-division multiple access (TDMA) strategy, in which at most one user can transmit in a slot, and propose a simple age-independent stationary randomized policy (AI-SRP). The AI-SRP makes transmission decisions based on the channel power gain realizations, without considering the AoIs. We then consider a more general non-orthogonal multiple access (NOMA) strategy, in which any number of users can transmit in a slot subject to capacity constraints of the MAC and propose an AI-SRP. The AI-SRPs we propose are optimal solutions to appropriate optimization problems. We show that the minimum achievable weighted average AoIs across the users under the proposed AI-SRPs are at most two times those of the respective optimal policies under TDMA and NOMA strategies.

The problem of decoding an (n, k, d) error-correcting block code, where a k-bit message word is mapped to an n-bit codeword, can be cast as a single-label classification problem. While it has been observed that the performance of such single-label neural decoders closely approaches that of the corresponding maximum likelihood decoder (MLD), the number of output nodes increases exponentially with k, making it prohibitive to implement for large k. To address this issue, we explore classification based multi-label neural decoders, in which the number of output nodes increases linearly with k. We consider well-known linear and non-linear block codes, as well as concatenated block codes, which have applications in emerging wireless networks. Our study finds that (i) although the number of output nodes linearly increases with k in a multi-label decoder, it requires more hidden layers and nodes in each hidden layer than the corresponding single-label decoder to achieve its best performance, and (ii) although one can design a multi-label decoder with bit error rate matching that of the MLD, it leaves more blocks in error leading to a reduced performance in terms of block error rate. We also note that the performance of the proposed decoder for concatenated codes is at least as good as that of a natural decoding algorithm in which the inner code is first decoded using the MLD and then the outer code is decoded with a polynomial-time decoding algorithm.

There has been a growing interest in designing neural-network based decoders (or neural decoders in short) for communication systems. In the prior work, we cast the problem of decoding an (n, k) block code as a single-label classification problem, and it is shown that the performance of such single-label neural decoders closely approaches that of the corresponding maximum likelihood soft-decision (ML-SD) decoders. The main issue is that the number of output nodes of single-label neural decoders increases exponentially with k, making it prohibitive to decode a code with medium or large dimension. To address this issue, we first explore a multi-label classification based neural decoder for block codes, in which the number of output nodes increases linearly with k. The complexity of the multi-label neural decoder is lower, but the performance is still close to that of the ML-SD decoder. We also consider concatenating a high-rate short-length outer code with the original code as the inner code. The proposed concatenated decoding architecture consists of a multi-label neural decoder for the inner code and a single label neural decoder for the outer code. The results demonstrate that the concatenated decoding approach leads to better bit and block error performance as compared to a benchmark soft-decision decoder. We note that the overall size of the concatenated neural decoder is close to that of the single-label neural decoder.

We consider the design of efficient neural-network based algorithms, referred to as neural decoders, for decoding linear and non-linear block codes, such as Hamming and constant-weight codes, respectively. Our goal is to study the impact of the number of layers and the number of hidden nodes in each layer on the performance and generalization ability of neural decoders. Specifically, we want to find the minimum number of hidden layers and the minimum number of hidden nodes in each layer required to achieve or closely approach the performance of the optimal maximum-likelihood soft-decision (ML-SD) decoder for a given code. For the linear block codes studied, we find that when the block-length is n, a neural network with a single hidden layer with n hidden units is necessary and sufficient to achieve the performance of the ML-SD decoder. For the non-linear block codes studied, a single hidden layer with n nodes results in performance that closely approaches that of the ML-SD decoder. In both the cases, we find that training at a signal-to-noise ratio (SNR) of 0 dB gives fairly good generalization ability, meaning that the neural decoder trained at an SNR of 0 dB works well across a wide range of SNR values.

In energy harvesting (EH) communications, it is customary to use a battery to temporarily store harvested energy prior to using it for communication. In practice, these batteries suffer from degradation in the usable capacity when they are repeatedly charged after being partially discharged and vice versa. The capacity can be recovered by imposing the full-cycle constraint, which says that a battery must be charged only after it is fully discharged and vice versa. Further, practical batteries cannot be charged and discharged simultaneously. With the above constraints, we consider and compare EH communication systems under two cases: (a) the single-battery case and (b) the dual-battery case, in which the transmitters are equipped with a single battery of capacity 2B joules and two batteries, each having capacity of B joules, respectively. Under (a) and (b), our goal is to obtain the long-term average throughputs and throughput regions in a point-to-point (P2P) channel and a multiple access channel (MAC), respectively. For the P2P channel, we derive the optimal solution in the single-battery case, and propose optimal and suboptimal power allocation policies for the dual-battery case, assuming Bernoulli energy arrivals. Based on these policies, we obtain long-term average achievable throughput regions in MACs by jointly allocating rates and powers. From numerical simulations, we find that the optimal throughput in the dual-battery case is significantly higher than that in the single-battery case, although the total storage capacity in both cases is 2B joules.

We consider a multiple-access channel (MAC), where transmitters are powered by energy harvesting. They are equipped with batteries having non-ideal charging and discharging characteristics, resulting in a fractional loss of power driven into or drawn from them. Assuming that each user consumes constant power for circuit operation during transmission, we optimize the throughput region, the set of all tuples of the number of bits delivered by the users over a finite duration of time. When circuit powers are zero, it is known that a non-orthogonal multiple access (NOMA) strategy, called Pure-NOMA (P-NOMA), where user transmissions always overlap, achieves all points on the largest throughput region. We show that P-NOMA is no longer optimal with non-zero circuit power and propose a hybrid strategy called H-NOMA that combines P-NOMA with time-division multiple access (TDMA). H-NOMA allocates fixed time windows for single-user and non-orthogonal multi-user transmissions. We maximize the sum-throughput in H-NOMA with non-casual and causal knowledge of the harvested powers and channel power gains. With causal knowledge, we obtain the optimal online policy via dynamic programming and deduce some structural properties and propose a simpler suboptimal online policy that performs significantly better than a naive greedy policy. We numerically show the largest throughput regions of P-NOMA and TDMA are contained within that of H-NOMA.

We consider a multiple-access channel where the users are powered from batteries having non-negligible internal resistance. When power is drawn from the battery, a variable fraction of the power, which is a function of the power drawn from the battery, is lost across the internal resistance. Hence, the power delivered to the load is less than the power drawn from the battery. The users consume a constant power for the circuit operation during transmission but do not consume any power when not transmitting. In this setting, we obtain the maximum sum-rates and achievable rate regions under various cases. We show that, unlike in the ideal battery case, the TDMA (time-division multiple access) strategy, wherein the users transmit orthogonally in time, may not always achieve the maximum sum-rate when the internal resistance is non-zero. The users may need to adopt a hybrid NOMA-TDMA strategy which combines the features of NOMA (non-orthogonal multiple access) and TDMA, wherein a set of users are allocated fixed time windows for orthogonal single-user and non-orthogonal joint transmissions. We also numerically show that the largest achievable rate regions in NOMA and TDMA strategies are contained within the largest achievable rate region of the hybrid NOMA-TDMA strategy.

Internet of Things (IoT) systems will increasingly rely on energy harvested from their environment, and energy harvesting (EH) techniques necessitate a rethinking of how we design and optimize IoT systems. The performance of EH IoT systems is affected by the battery nonidealities and the energy consumption for transmitting and receiving. While EH considerations at the transmitter have been widely studied, the EH receiver has received relatively much less attention. Motivated by this, we investigate, in this paper, the performance of EH receivers in IoT systems with batteries having non-negligible internal resistance. We first consider a receiver with a dual-path architecture and give an optimal battery management scheme. Then, based on this management scheme, we maximize the amount of information decoded at the receiver for single and multiple block scenarios. In the multiple block scenario, we transform the nonconvex problem into a series of convex problems by exploiting certain structural properties of the nonconvex constraints. Additionally, we present extensive numerical results to validate our analysis and to study the impact of the internal resistance. This paper suggests that the internal resistance significantly impacts the design and performance of EH IoT systems. However, the dual-path architecture can be an efficient way to reduce the performance loss caused by internal resistance. Finally, we discuss implementation considerations.

We consider rate maximization for an energy harvesting node transmitting delay-constrained information over a slow fading channel corrupted by additive white Gaussian noise. Time is divided into frames of fixed duration equal to the channel coherence block length, the time duration for which the channel power gain remains constant before changing to a different value, independently. We assume that the transmitter does not know the exact channel state but has access to the channel statistics. The transmitter is equipped with a battery having non-zero internal resistance. Using superposition coding, we formulate and study an average rate maximization problem with non-causal knowledge of the harvested power. Further, assuming statistical knowledge and causal information of the harvested power variations, we propose a sub-optimal algorithm, and compare with the stochastic dynamic programming based solution and a greedy policy.

Modern systems will increasingly rely on energy harvested from their environment. Such systems utilize batteries to smooth out the random fluctuations in harvested energy. These fluctuations induce highly variable battery charge and discharge rates, which affect the efficiencies of practical batteries that typically have non-zero internal resistance. In this paper, we study an energy harvesting communication system using a finite battery with non-zero internal resistance. We adopt a dual-path architecture, in which harvested energy can be directly used, or stored and then used. In a frame, both time and power can be split between energy storage and data transmission. For a single frame, we derive an analytical expression for the rate optimal time and power splitting ratios between harvesting energy and transmitting data. We then optimize the time and power splitting ratios for a group of frames, assuming non-causal knowledge of harvested power and fading channel gains, by giving an approximate solution. When only the statistics of the energy arrivals and channel gains are known, we derive a dynamic programming-based policy and propose three sub-optimal policies, which are shown to perform competitively. In summary, this paper suggests that battery internal resistance significantly impacts the design and performance of energy harvesting communication systems and must be considered.

We consider the design of energy management policies for multimedia wireless sensor nodes that rely entirely on harvesting energy from the environment for both the data acquisition and transmission. In many high volume data sensing applications, the sampled data is compressed before transmission to meet the bandwidth and transmit power constraints. The compression results in data distortion, but it reduces the amount of data to be transmitted. As a consequence, the transmission energy is reduced, but excessive compression may consume more energy than what is saved by transmitting less data. This points to a trade-off between compression and transmission (in terms of both the energy and time allocated to these operations). Our goal is to identify the optimal energy management policies that minimize the long-term average distortion at the receiver. We first study the optimal solution in an off-line setting and then propose three on-line policies. We highlight the importance of the compression power, showing that, all other system parameters being equal, the average distortion decreases exponentially as the compression power is increased by processing at a faster rate.

We consider the design of transmission policies for sensor nodes that rely entirely on harvesting energy from the environment. Nodes store the harvested energy in a storage element which has constraints on maximum discharge rate and charging efficiency. Non-zero circuit power is considered and limitations on channel bandwidth and processor clock-rate are incorporated. We assume an additive white Gaussian noise (AWGN) channel and that time is divided into frames, with a fixed number of symbols transmitted in the frame duration. We consider an energy arrival process in which energy arrives at a constant rate within a frame but varies stochastically and independently across frames. In this context, we propose a dual-path architecture for energy flow that is shown to mitigate the performance loss due to the discharge rate constraint. For a given frame, we determine the rate-optimal time sharing ratio between harvesting energy and transmitting data. We also propose three sub-optimal policies, including statistical directional water-filling, for determining the time sharing ratio for a group of frames and compare their performance with an upper bound. We highlight that the discharge rate constraint is an important limitation of the storage element that can potentially hinder the effective use of energy.