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This paper presents a novel approach to solving convex optimization problems by leveraging the fact that, under certain regularity conditions, any set of primal or dual variables satisfying the Karush-Kuhn-Tucker (KKT) conditions is necessary and sufficient for optimality. Similar to Theory-Trained Neural Networks (TTNNs), the parameters of the convex optimization problem are input to the neural network, and the expected outputs are the optimal primal and dual variables. A choice for the loss function in this case is a loss, which we refer to as the KKT Loss, that measures how well the network's outputs satisfy the KKT conditions. We demonstrate the effectiveness of this approach using a linear program as an example. For this problem, we observe that minimizing the KKT Loss alone outperforms training the network with a weighted sum of the KKT Loss and a Data Loss (the mean-squared error between the ground truth optimal solutions and the network's output). Moreover, minimizing only the Data Loss yields inferior results compared to those obtained by minimizing the KKT Loss. While the approach is promising, the obtained primal and dual solutions are not sufficiently close to the ground truth optimal solutions. In the future, we aim to develop improved models to obtain solutions closer to the ground truth and extend the approach to other problem classes.

In next-generation wireless networks, low latency often necessitates short-length codewords that either do not use channel state information (CSI) or rely solely on CSI at the receiver (CSIR). Gaussian codes that achieve capacity for AWGN channels may be unsuitable for these no-CSI and CSIR-only cases. In this work, we design short-length codewords for these cases using an autoencoder architecture. From the designed codes, we observe the following: In the no-CSI case, the learned codes are mutually orthogonal when the distribution of the real and imaginary parts of the fading random variable has support over the entire real line. However, when the support is limited to the non-negative real line, the codes are not mutually orthogonal. For the CSIR-only case, deep learning-based codes designed for AWGN channels perform worse in fading channels with optimal coherent detection compared to codes specifically designed for fading channels with CSIR, where the autoencoder jointly learns encoding, coherent combining, and decoding. In both no-CSI and CSIR-only cases, the codes perform at least as well as or better than classical codes of the same block length.

We consider the communication of natural language text from a source to a destination over noiseless and character-erasure channels. We exploit language's inherent correlations and predictability to constrain transmission costs by allowing the destination to predict or complete words with potential dissimilarity with the source text. Concretely, our objective is to obtain achievable $(\bar{c}, \bar{s})$ pairs, where $\bar{c}$ is the average transmission cost at the source and $\bar{s}$ is the average semantic similarity measured via cosine similarity between vector embedding of words at the source and those predicted/completed at the destination. We obtain $(\bar{c}, \bar{s})$ pairs for neural language and first-order Markov chain-based small language models (SLM) for prediction, using both a threshold policy that transmits a word if its cosine similarity with that predicted/completed at the destination is below a threshold, and a periodic policy, which transmits words after a specific interval and predicts/completes the words in between, at the destination. We adopt an SLM for word completion. We demonstrate that, when communication occurs over a noiseless channel, the threshold policy achieves a higher $\bar{s}$ for a given $\bar{c}$ than the periodic policy and that the $\bar{s}$ achieved with the neural SLM is greater than or equal to that of the Markov chain-based algorithm for the same $\bar{c}$. The improved performance comes with a higher complexity in terms of time and computing requirements. However, when communication occurs over a character-erasure channel, all prediction algorithms and scheduling policies perform poorly. Furthermore, if character-level Huffman coding is used, the required $\bar{c}$ to achieve a given $\bar{s}$ is reduced, but the above observations still apply.

We consider a base station (BS) that receives version update packets from multiple exogenous streams and broadcasts them to corresponding users over a fading broadcast channel using a non-orthogonal multiple access (NOMA) scheme. Sequentially indexed packets arrive randomly in each stream, with new packets making the previous ones obsolete. In this case, we consider the version age of information (VAoI) at a user, defined as the difference in the version index of the latest available packet at the BS and that at the user, as a metric of freshness of information. Our objective is to minimize a weighted sum of average VAoI across users subject to an average power constraint at the BS by optimally scheduling the update packets from various streams for transmission and transmitting them with sufficient powers to guarantee their successful delivery. We consider the class of channel-only stationary randomized policies (CO-SRP), which rely solely on channel power gains for transmission decisions. We solve the resulting non-convex problem optimally and show that the VAoI achieved under the optimal CO-SRP is within twice the optimal achievable VAoI. We also obtained a Constrained Markov Decision Process (CMDP)-based solution and its structural properties. Numerical simulations show a close performance between the optimal CO-SRP and CMDP-based solutions. Additionally, a time division multiple access (TDMA) scheme, which allows transmission to at most one user at a time, matches NOMA's performance under tight average power constraints. However, NOMA outperforms TDMA as the constraint is relaxed.

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. Finally, we conclude that prior AoI optimization literature with finite blocklengths substantially underestimates AoI because they assume that all errors can be detected perfectly without using CRC.

The problem of packing smaller objects within a larger object has been of interest since decades. 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.

We consider a scenario where multiple users, powered by energy harvesting, send version updates over a fading multiple access channel (MAC) to an access point (AP). Version updates having random importance weights arrive at a user according to an exogenous arrival process, and a new version renders all previous versions obsolete. As energy harvesting imposes a time-varying peak power constraint, it is not possible to deliver all the bits of a version instantaneously. Accordingly, the AP chooses the objective of minimizing a finite-horizon time average expectation of the product of importance weight and a convex increasing function of the number of remaining bits of a version to be transmitted at each time instant. The objective enables importance-aware delivery of as many bits, as soon as possible. In this setup, the AP optimizes the objective function subject to an achievable rate-region constraint of the MAC and energy constraints at the users, by deciding the transmit power and the number of bits to be transmitted by each user. We obtain a Markov Decision Process (MDP)-based optimal online policy to the problem and derive structural properties of the policy. We then develop a neural network (NN)-based online heuristic policy, for which we train an NN on the optimal offline policy derived for different sample paths of energy, version arrival and channel power gain processes. Via numerical simulations, we observe that the NN-based online policy performs competitively with respect to the MDP-based online policy.

We consider a source monitoring a stochastic process with a transmitter to transmit timely information through a wireless ON/OFF channel to a destination. We assume that once the source samples the data, the sampled data has to be processed to identify the state of the stochastic process. The processing can take place either at the source before transmission or after transmission at the destination. The objective is to minimize the distortion while keeping the age of information (AoI) that measures the timeliness of information under a certain threshold. We use a stationary randomized policy (SRP) framework to solve the formulated problem. We show that the two-dimensional discrete-time Markov chain considering the AoI and instantaneous distortion as the state is lumpable and we obtain the expression for the expected AoI under the SRP., Comment: 8 pages, 6 figures

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.