A linear neural network computes a linear transformation of its input vector. Given a fully-connected linear network, the set of all weight vectors for which the network computes the same linear transformation is an algebraic variety in weight space, called a fiber under the matrix multiplication map. Sometimes this variety is a manifold, but usually not. The rank stratification of a fiber is a natural partition of the fiber into manifolds of various dimensions called strata. We characterize how these strata are connected to each other. They satisfy the frontier condition: if a stratum intersects the closure of another stratum, then the former stratum is a subset of the closure of the latter stratum. This subset relationship can be expressed as a partial order with a single minimal element. Our main result describes the relationship between this partial order and the ranks of certain matrices in the network. Each stratum represents a different pattern of information flow through the network, expressed as a barcode. Connections among the strata are best understood through simple transformations of the barcodes called barcode moves.

Accurate and efficient estimation of Channel State Information (CSI) is critical for next-generation wireless systems operating under non-stationary conditions, where user mobility, Doppler spread, and multipath dynamics rapidly alter channel statistics. Conventional pilot aided estimators incur substantial overhead, while deep learning approaches degrade under dynamic pilot patterns and time varying fading. This paper presents a pilot-aided Flash-Attention Transformer framework that unifies model-driven pilot acquisition with data driven CSI reconstruction through patch-wise self-attention and a physics aware composite loss function enforcing phase alignment, correlation consistency, and time frequency smoothness. Under a standardized 3GPP NR configuration, the proposed framework outperforms LMMSE and LSTM baselines by approximately 13 dB in phase invariant normalized mean-square error (NMSE) with markedly lower bit-error rate (BER), while reducing pilot overhead by 16 times. These results demonstrate that attention based architectures enable reliable CSI recovery and enhanced spectral efficiency without compromising link quality, addressing a fundamental bottleneck in adaptive, low-overhead channel estimation for non-stationary 5G and beyond-5G networks.

We introduce the genuine multipartite Rains entanglement (GMRE) as a measure of genuine multipartite entanglement that can be computed using semi-definite programming. Similar to the Rains relative entropy (its bipartite counterpart), the GMRE is monotone under selective quantum operations that completely preserve the positivity of the partial transpose, implying that it is a multipartite entanglement monotone. As a consequence, we show that the GMRE bounds both the one-shot standard and probabilistic approximate GHZ-distillable entanglement from above. We also develop a generalization of this quantity that incorporates other entropies, including quantum Renyi relative entropies.

6G envisions massive cell-free networks with spatially nested multiple access (MAC) and broadcast (BC) channels without centralized coordination. This renders optimal resource allocation—across power, subcarriers, and decoding orders crucial for interference channels (ICs), where neither transmitters nor receivers can cooperate. Current orthogonal multiple access (OMA) methods, as well as non-orthogonal (NOMA) and rate-splitting (RSMA) schemes, rely on fixed heuristics for interference management, leading to suboptimal rates, power inefficiency, and scalability issues. This paper proposes a novel minPIC framework for optimal power, subcarrier, and decoding order allocation in general multi-user ICs. Unlike existing methods, minPIC eliminates heuristic SIC order assumptions. Despite the convexity of the IC capacity region, fixing an SIC order induces non-convexity in resource allocation, traditionally requiring heuristic approximations. We instead introduce a dual-variable-guided sorting criterion to identify globally optimal SIC orders, followed by convex optimization with auxiliary log-det constraints, efficiently solved via binary search. We also demonstrate that minPIC could potentially meet the stringent high-rate, low-power targets of immersive XR and other 6G applications. To the best of our knowledge, minPIC is the first algorithmic realisation of the Pareto boundary of the SIC-achievable rate region for Gaussian ICs, opening the door to scalable interference management in cell-free networks.

Next-generation IoT and cyber-physical systems must deliver fresh updates while keeping queues stable and radios energy-frugal. Existing backlog-centric schedulers minimize delay but ignore data freshness, whereas age-centric policies risk throughput collapse. This work proposes AoI-Queue-Proportional Scheduling (AOI-QPS), an energy-aware extension of classical QPS that allocates service proportional to a weighted sum of queue lengths and Age-of-Information. A Lyapunov-drift analysis proves AOI-QPS is throughput-optimal and bounds average AoI by $\mathcal{O}(1/\alpha )$ while guaranteeing finite delay. Incorporating a IEEE802.15.4-derived energy model further yields an empirical AoI-per-Joule guarantee for queue-stable policies. Extensive simulations under uniform, skewed, and bursty traffic show AOI-QPS cuts network-wide AoI by up to 60% versus QPS, matches Max-AoI’s freshness within 5%, and eliminates the 30% idle-slot energy waste of static schedulers—all without sacrificing queue stability or energy efficiency. AOI-QPS thus addresses the AoI–queue–energy trade-off, offering a practical, analytically grounded knob for balancing freshness, latency, and sustainability in next-generation wireless networks.

This paper proposes a novel joint channel-estimation and source-detection algorithm using successive interference cancellation (SIC)-aided generative score-based diffusion models. Prior work in this area focuses on massive MIMO scenarios, which are typically characterized by full-rank channels, and fail in low-rank channel scenarios. The proposed algorithm outperforms existing methods in joint source-channel estimation, especially in low-rank scenarios where the number of users exceeds the number of antennas at the access point (AP). The proposed score-based iterative diffusion process estimates the gradient of the prior distribution on partial channels, and recursively updates the estimated channel parts as well as the source. Extensive simulation results show that the proposed method outperforms the baseline methods in terms of normalized mean squared error (NMSE) and symbol error rate (SER) in both full-rank and low-rank channel scenarios, while having a more dominant effect in the latter, at various signal-to-noise ratios (SNR).

Currently used resource allocation methods for uplink multicarrier non-orthogonal multiple access (MC-NOMA) systems have multiple shortcomings. Current approaches either allocate the same power across all subcarriers to a user, or use heuristic-based near-far, strong channel-weak channel user grouping to assign the decoding order for successive interference cancellation (SIC). This paper proposes a novel optimal power-subcarrier allocation for uplink MC-NOMA. This new allocation achieves the optimal power-subcarrier allocation as well as the optimal SIC decoding order. Furthermore, the proposed method includes a time-sharing algorithm that dynamically alters the decoding orders of the participating users to achieve the required data rates, even in cases where any single decoding order fails to do so. Extensive experimental evaluations show that the new method achieves higher sum data rates and lower power consumption compared to current NOMA methods.

Upcoming Augmented Reality (AR) and Virtual Reality (VR) systems require high data rates ($\geq \mathbf{500 Mbps}$) and low power consumption for seamless experience. With an increasing number of subscribing users, the total number of antennas across all transmitting users far exceeds the number of antennas at the access point (AP). This results in a low rank wireless channel, presenting a bottleneck for uplink communication systems. The current uplink systems that use orthogonal multiple access (OMA) and the proposed non-orthogonal multiple access (NOMA), fail to achieve the required data rates / power consumption under predominantly low rank channel scenarios. This paper introduces an optimal power sub carrier allocation algorithm for multicarrier NOMA, named minPMAC, and an associated timesharing algorithm that adaptively changes successive interference cancellation decoding orders to maximize sum data rates in these low rank channels. This Lagrangian based optimization technique, although globally optimum, is prohibitive in terms of runtime, proving inefficient for real-time scenarios. Hence, we propose a novel near-optimal deep reinforcement learningbased energy sum optimization (DRL-minPMAC) which achieves real-time efficiency. Extensive experimental evaluations show that minPMAC achieves$\mathbf{2 8 \%}$and 39% higher data rates than NOMA and OMA baselines. Furthermore, the proposed DRL-minPMAC runs 5 times faster than minPMAC and achieves 83% of the global optimum data rates in real time.*

Inspired by classical shared information and multiterminal squashed entanglement, we introduce shared squashed entanglement, a new measure of multiterminal quantum entanglement that is also an LOCC monotone and tighter than multiterminal squashed entanglement. We also introduce a class of quantum source models, called quantum pairwise independent network (PIN) models, consisting of pairs of terminals sharing mutually independent Bell-pairs between them. We find lower and upper bounds for the amount of entanglement that can be distilled from quantum PIN models. For specific quantum PIN models, our proposed upper bound matches our achievability result, whereas squashed entanglement does not.

Recent advances in symbolic music generation primarily rely on deep learning models such as Transformers, GANs, and diffusion models. While these approaches achieve high-quality results, they require substantial computational resources, limiting their scalability. We introduce LZMidi, a lightweight symbolic music generation framework based on a Lempel-Ziv (LZ78)-induced sequential probability assignment (SPA). By leveraging the discrete and sequential structure of MIDI data, our approach enables efficient music generation on standard CPUs with minimal training and inference costs. Theoretically, we establish universal convergence guarantees for our approach, underscoring its reliability and robustness. Compared to state-of-the-art diffusion models, LZMidi achieves competitive Fréchet Audio Distance (FAD), Wasserstein Distance (WD), and Kullback-Leibler (KL) scores, while significantly reducing computational overhead-up to$30 \times$faster training and$300 \times$faster generation. Our results position LZMidi as a significant advancement in compression-based learning, highlighting how universal compression techniques can efficiently model and generate structured sequential data, such as symbolic music, with practical scalability and theoretical rigor.

Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. Firstly, many approaches rely on modeling continuous embeddings, which is suboptimal for inherently discrete data distributions. Secondly, most models optimize variational bounds rather than exact data likelihood, resulting in inaccurate likelihood estimates and degraded sampling quality. While recent diffusion-based models have addressed these issues separately, we tackle them jointly. In this work, we introduce the Information-Theoretic Discrete Poisson Diffusion Model (ItDPDM), inspired by photon arrival process, which combines exact likelihood estimation with fully discrete-state modeling. Central to our approach is an information-theoretic Poisson Reconstruction Loss (PRL) that has a provable exact relationship with the true data likelihood. ItDPDM achieves improved likelihood and sampling performance over prior discrete and continuous diffusion models on a variety of synthetic discrete datasets. Furthermore, on real-world datasets such as symbolic music and images, ItDPDM attains superior likelihood estimates and competitive generation quality—demonstrating a proof of concept for distribution-robust discrete generative modeling.

Recently, Ultra-wideband (UWB) chips have started to be integrated into smartphones. Since UWB has advantage of high distance measurement accuracy, UWB can be utilized for spatial awareness services. Thus, many companies are preparing for UWB-based services. However, the upcoming future services are mainly conducted indoors and require high localization accuracy. This poses a challenge for UWB technology because indoor environments contain various factors that can interfere UWB signals and degrade localization accuracy. Therefore, a method to mitigate the Non-Line-of-Sight (NLOS) problem and maintain high localization accuracy is necessary. In this paper we propose NDA, an NLOS-robust Downlink Time-Difference-of-Arrival (DL-TDOA) localization method using adaptive anchor selection. NDA classifies the channel condition of anchors using Channel Impulse Response (CIR), and TDOA measurements are validated through outlier detection. Anchor selection is performed considering the channel condition and the convex hull of Mobile Device (MD). NDA is implemented on a smartphone and UWB module for real-world experiment. Experiment results under NLOS conditions showed improved localization accuracy of 62% when MD is stationary and 20% when MD is dynamic.

In this paper, to efficiently support virtual reality (VR) and extended reality (XR) applications, we propose a novel method for gesture recognition utilizing inertial measurement unit (IMU) and ultra-wideband (UWB) in the commercial off-the-shelf, where three smartphones are used for one head mounted display (HMD) and two wrist-attached devices (WADs). According to the intensive experimental evaluations, our proposed method can provide very high success rate of gesture recognition for pre-defined 10 hand motions. For 8 volunteers participating the data collection, classifier learning, and testing, we observed that the recognition success rate of 100 % is achieved. Moreover, the success rate of 91.9% for new users who did not participate in learning can be achieved. These results can provide meaningful guidelines to adopt the UWB chipset into the HMD and WADs, because UWB significantly improves the success rate of gesture recognition than that result from the IMU only.

Shared information is a measure of mutual dependence among$m\geq 2$jointly distributed discrete random variables. We show that the shared information of a Markov random field in which the underlying graph has at least one cut vertex, is the same as the minimum shared information of its blocks (also called biconnected components). This generalizes prior results on shared information of Markov random fields to a much wider class of nontree graphs.

Shared information is a measure of mutual dependence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. The Markov chain on a tree is shown to possess a global Markov property based on graph separation; this property plays a key role in our proofs. When the underlying joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance.

Among the various Ultra-wideband (UWB) ranging methods, the absence of uplink communication or centralized computation makes downlink time-difference-of-arrival (DL-TDOA) localization the most suitable for large-scale industrial deployments. However, temporary or permanent obstacles in the deployment region often lead to non-line-of-sight (NLOS) channel path and signal outage effects, which result in localization errors. Prior research has addressed this problem by increasing the ranging frequency, which leads to a heavy increase in the user device power consumption. It also does not contribute to any increase in localization accuracy under line-of-sight (LOS) conditions. In this paper, we propose and implement a novel low-power channel-aware dynamic frequency DL-TDOA ranging algorithm. It comprises NLOS probability predictor based on a convolutional neural network (CNN), a dynamic ranging frequency control module, and an IMU sensor-based ranging filter. Based on the conducted experiments, we show that the proposed algorithm achieves 50% higher accuracy in NLOS conditions while having 46% lower power consumption in LOS conditions compared to baseline methods from prior research.

As commercial interest in proximity services in-creased, the development of various wireless localization techniques was promoted. In line with this trend, Ultra-wideband (UWB) is emerging as a promising solution that can realize proximity services thanks to centimeter-level localization accuracy. In addition, since the actual location of the mobile device (MD) on the human body, called pose, affects the localization accuracy, poses are also important to provide accurate proximity services, especially for the UWB tagless gate (UTG). In this paper, a real-time pose detector, termed D3, is proposed to estimate the pose of MD when users pass through UTG. D3 is based on line-of-sight (LOS) and non-LOS (NLOS) classification using UWB channel impulse response and utilizes the inertial measurement unit embedded in smartphone to estimate the pose. D3 is implemented on Samsung Galaxy Note20 Ultra (i.e., SM-N986B) and Qorvo UWB board to show the feasibility and applicability. D3 achieved an LOS/NLOS classification accuracy of 0.984, and ultimately detected four different poses of MD with an accuracy of 0.961 in real-time.

Shared information is a measure of mutual dependence among m≥2 jointly distributed discrete random variables. A new undirected probabilistic graphical model, a cliqueylon graph, is introduced, with potential applications in leader-follower swarms and neuron clusters with correlations of varying strength. Shared information is characterized explicitly for the cliqueylon, relying on structural properties of an underlying optimization. Implications for the data compression problem of omniscience are highlighted.

One of the crucial factors in improving the localization performance of an Ultra-wideband (UWB) downlink time-difference-of-arrival (DL-TDOA) system is the optimal location planning and cluster assignment of the UWB anchors. Prior research takes into account the dilution-of-precision (DOP) or the anchor-user device channel conditions, to solve the anchor location planning. However they do not consider the joint cluster assignment problem, and thus do not include the DL-TDOA cluster-specific metrics to optimize the anchor locations. This often leads to intra-cluster anchor-anchor clock offset related errors affecting the overall performance of DL-TDOA localization. In this paper, we propose a novel joint anchor location planning and cluster assignment algorithm for DL-TDOA. We not only take into account the anchor-user device channel conditions and the DOP, but also the channel conditions between anchors of the same cluster, which may lead to anchor-anchor clock offset based ranging errors. The simulation results show that our proposed algorithm achieves lower average localization error compared to baseline methods derived from prior research, as well as lower values of anchor-anchor clock offset based error, while having a fairly low computational complexity.

Shared information is a measure of mutual dependence among m ≥ 2 jointly distributed discrete random variables. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. When the joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance.

Consider a finite set of multiple sources, described by a random variable with$m$components. Only$k\leq m$source components are sampled and jointly compressed in order to reconstruct all the$m$components under an excess distortion criterion. Sampling can be that of a fixed subset$A$with$\vert A\vert =k$or randomized over all subsets of size$k$. In the case of random sampling, the sampler may or may not be aware of the$m$source components. The compression code consists of an encoder whose input is the realization of the sampler and the sampled source components; the decoder input is solely the encoder output. The combined sampling mechanism and rate distortion code are universal in that they must be devised without exact knowledge of the prevailing source probability distribution. In a Bayesian setting, considering coordinated single-shot sampling and compression, our contributions involve achievability results for the cases of fixed-set, source-independent and source-dependent random sampling.

We develop general techniques to bound the size of the balls of a given radius r for q-ary discrete metrics, using the generating function for the metric and Sanov's theorem, that reduces to the known bound in the case of the Hamming metric and gives us a new bound in the case of the Lee metric. We use the techniques developed to find Hamming, Elias-Bassalygo and Gilbert-Varshamov bounds for the Lee metric.

We study an adversarial communication problem where sender Alice wishes to send a message m to receiver Bob over an arbitrarily varying channel (AVC) controlled by a malicious adversary James. We assume that Alice and Bob share randomness K unknown to James. Using K, Alice first encodes the message m to a codeword X and transmits it over the AVC. James knows the message m, the (randomized) codebook and the codeword X. James then inputs a jamming state S to disrupt communication; we assume a state-deterministic AVC where S completely specifies the channel noise. Bob receives a noisy version Y of codeword X; it outputs a message estimate m using Y and the shared randomness K. We study AVCs, called `adversary-weakened' AVCs here, where the availability of shared randomness strictly improves the optimum throughput or capacity over it than when it is not available; the randomized coding capacity characterizes the largest rate possible when K is unrestricted. In this work, we characterize the exact threshold for the amount of shared randomness K so as to achieve the randomized coding capacity for `adversary-weakened' AVCs. We show that exactly log(n) equiprobable and independent bits of randomness, shared between Alice and Bob and unknown to adversary James, are both necessary and sufficient for achieving randomized coding capacity for `adversary-weakened' AVCs. For sufficiency, our achievability is based on a randomized code construction which uses deterministic list codes along with a polynomial hashing technique which uses the shared randomness. Our converse, which establishes the necessity of log(n) bits of shared randomness, uses a known approach for binary AVCs, and extends it to general `adversary-weakened' AVCs using a notion of confusable codewords.

In recent years, large distributed sensor networks have emerged as a new fast-growing application domain for wireless computing. In this paper, we present a distributed application-layer service for data placement and asynchronous multicast whose purpose is power conservation. Since the dominant traffic in a sensor network is that of data retrieval, (i) caching mutable data at locations that minimize the sum of request and update traffic, and (ii) asynchronously multicasting updates from sensors to observers can significantly reduce the total number of packet transmissions in the network. Our simulation results show that our service subsequently reduces network energy consumption while maintaining the desired data consistency semantics.