arXiv subjects

Chih-Chun Wang

Publications and source records attributed to Chih-Chun Wang.

At least 19 recordsLinked to original sources

arXiv2026

Unified Framework for Functional Theories of Quantum Systems

We introduce and study a unified framework for density-functional theory and its variants for quantum systems on finite-dimensional Hilbert spaces. These theories seek to reduce the complexity inherent in the many-body quantum problem by describing ground states through reduced variables. The central ingredients of our unified framework are a generalized choice of basic observables, whose expectation values define precisely those reduced variables, and a fixed part of the Hamiltonian characterizing the class of quantum systems under consideration. It is this minimal structure, which we call the scope of a functional theory, that is necessary and sufficient for the formulation of a functional theory. In particular, it allows one to define the universal functionals, establish their convexity and differentiability properties, address representability questions, and prove a Hohenberg-Kohn-type uniqueness result. A purification construction also relates ensemble and weighted-ensemble functionals to the pure-state variant. Particular emphasis is placed on functional theories with Lie-algebra observable structures, connecting the variational framework to symplectic geometry. The result of this work is a systematic mathematical formulation in which structural results can be proved once and applied across a broad class of finite-dimensional functional theories.

math-ph↗

arXiv2026

Geometry of Generalized Density Functional Theories

Density functional theory (DFT) is an indispensable ab initio method in both quantum chemistry and condensed matter physics. Based on recent advancements in reduced density matrix functional theory (RDMFT), a variant of DFT that is believed to be better suited for strongly correlated systems, we construct a mathematical framework generalizing all ground state functional theories, which in particular applies to fermionic, bosonic, and spin systems. Within the special class of such functional theories where the space of external potentials forms the Lie algebra of a compact Lie group, the $N$-representability problem is readily solved by applying techniques from the study of momentum maps in symplectic geometry, an approach complementary to Klyachko's famous solution to the quantum marginal problem. The ``boundary force'', a diverging repulsive force from the boundary of the functional's domain observed in previous works but only qualitatively understood in isolated systems, is studied quantitatively and extensively in our work. Specifically, we present a formula capturing the exact behavior of the functional close to the boundary. In the case where the Lie algebra is abelian, a completely rigorous proof of the boundary force formula based on Levy-Lieb constrained search is given. Our formula is a first step towards developing more accurate functional approximations, with the potential of improving current RDMFT approximate functionals such as the Piris natural orbital functionals (NOFs). All key concepts and ideas of our work are demonstrated in translation invariant bosonic lattice systems.

quant-ph↗

arXiv2026

Beyond Freshness and Semantics: A Coupon-Collector Framework for Effective Status Updates

For status update systems operating over unreliable energy-constrained wireless channels, we address Weaver's long-standing Level-C question: do my packets actually improve the plant's behavior? Each fresh sample carries a stochastic expiration time -- governed by the plant's instability dynamics -- after which the information becomes useless for control. Casting the problem as a coupon-collector variant with expiring coupons, we (i) formulate a two-dimensional average-reward MDP, (ii) prove that the optimal schedule is doubly thresholded in the receiver's freshness timer and the sender's stored lifetime, (iii) derive a closed-form policy for deterministic lifetimes, and (iv) design a Structure-Aware Q-learning algorithm (SAQ) that learns the optimal policy without knowing the channel success probability or lifetime distribution. Simulations validate our theoretical predictions: SAQ matches optimal Value Iteration performance while converging significantly faster than baseline Q-learning, and expiration-aware scheduling achieves up to 50% higher reward than age-based baselines by adapting transmissions to state-dependent urgency -- thereby delivering Level-C effectiveness under tight resource constraints.

eess.SY↗

arXiv2026

A Geometric Approach to Strongly Correlated Bosons: From $N$-Representability to the Generalized BEC Force

Building on recent advances in reduced density matrix theory, we develop a geometric framework for describing strongly correlated lattice bosons. We first establish that translational symmetry, together with a fixed pair interaction, enables an exact functional formulation expressed solely in terms of momentum occupation numbers. Employing the constrained-search formalism and exploiting a geometric correspondence between $N$-boson configuration states and their one-particle reduced density matrices, we derive the general form of the ground-state functional. Its structure highlights the omnipresent significance of one-body $N$-representability: (i) the domain is exactly determined by the $N$-representability conditions; (ii) at its boundary, the gradient of the functional diverges repulsively, thereby generalizing the recently discovered Bose-Einstein condensate (BEC) force; and (iii) an explicit expression for this boundary force follows directly from geometric arguments. These key results are demonstrated analytically for few-site lattice systems, and we illustrate the broader significance of our functional form in defining a systematic hierarchy of functional approximations.

quant-ph↗

arXiv2025

Deep Broadcast Feedback Codes

Recent advances in deep learning for wireless communications have renewed interest in channel output feedback codes. In the additive white Gaussian broadcast channel with feedback (AWGN-BC-F), feedback can expand the channel capacity region beyond that of the no-feedback case, but linear analytical codes perform poorly with even small amounts of feedback noise. Deep learning enables the design of nonlinear feedback codes that are more resilient to feedback noise. We extend single-user learned feedback codes for the AWGN channel to the broadcast setting, and compare their performance with existing analytical codes, as well as a newly proposed analytical scheme inspired by the learned schemes. Our results show that, for a fixed code rate, learned codes outperform analytical codes at the same blocklength by using power-efficient nonlinear structures and are more robust to feedback noise. Analytical codes scale more easily to larger blocklengths with perfect feedback and surpass learned codes at higher SNRs.

eess.SP↗

arXiv2024

Ambient IoT: Communications Enabling Precision Agriculture

One of the most intriguing 6G vertical markets is precision agriculture, where communications, sensing, control, and robotics technologies are used to improve agricultural outputs and decrease environmental impact. Ambient IoT (A-IoT), which uses a network of devices that harvest ambient energy to enable communications, is expected to play an important role in agricultural use cases due to its low costs, simplicity, and battery-free (or battery-assisted) operation. In this paper, we review the use cases of precision agriculture and discuss the challenges. We discuss how A-IoT can be used for precision agriculture and compare it with other ambient energy source technologies. We also discuss research directions related to both A-IoT and precision agriculture.

eess.SP↗

arXiv2023

Channel Capacity for Adversaries with Computationally Bounded Observations

We study reliable communication over point-to-point adversarial channels in which the adversary can observe the transmitted codeword via some function that takes the $n$-bit codeword as input and computes an $rn$-bit output for some given $r \in [0,1]$. We consider the scenario where the $rn$-bit observation is computationally bounded -- the adversary is free to choose an arbitrary observation function as long as the function can be computed using a polynomial amount of computational resources. This observation-based restriction differs from conventional channel-based computational limitations, where in the later case, the resource limitation applies to the computation of the (adversarial) channel error. For all $r \in [0,1-H(p)]$ where $H(\cdot)$ is the binary entropy function and $p$ is the adversary's error budget, we characterize the capacity of the above channel. For this range of $r$, we find that the capacity is identical to the completely obvious setting ($r=0$). This result can be viewed as a generalization of known results on myopic adversaries and channels with active eavesdroppers for which the observation process depends on a fixed distribution and fixed-linear structure, respectively, that cannot be chosen arbitrarily by the adversary.

cs.IT↗

arXiv2023

Challenges and Opportunities for Beyond-5G Wireless Security

The demand for broadband wireless access is driving research and standardization of 5G and beyond-5G wireless systems. In this paper, we aim to identify emerging security challenges for these wireless systems and pose multiple research areas to address these challenges.

eess.SY↗

arXiv2023

Age Minimization with Energy and Distortion Constraints

In this paper, we consider a status update system, where an access point collects measurements from multiple sensors that monitor a common physical process, fuses them, and transmits the aggregated sample to the destination over an erasure channel. Under a typical information fusion scheme, the distortion of the fused sample is inversely proportional to the number of measurements received. Our goal is to minimize the long-term average age while satisfying the average energy and general age-based distortion requirements. Specifically, we focus on the setting in which the distortion requirement is stricter when the age of the update is older. We show that the optimal policy is a mixture of two stationary, deterministic, threshold-based policies, each of which is optimal for a parameterized problem that aims to minimize the weighted sum of the age and energy under the distortion constraint. We then derive analytically the associated optimal average age-cost function and characterize its performance in the large threshold regime, the results of which shed critical insights on the tradeoff among age, energy, and the distortion of the samples. We have also developed a closed-form solution for the special case when the distortion requirement is independent of the age, arguably the most important setting for practical applications.

cs.IT↗

arXiv2018

Flexible Fractional Repetition Codes for Distributed Storage Networks

Consider the following fundamental question of distributed storage networks: Given any arbitrary $(n,k,d)$ values, whether there exists an intelligent helper selection scheme (assuming unlimited memory and computing power) that can strictly improve the storage-bandwidth (S-B) tradeoff. Ahmad et al. 18' answered this question by proving that for a subset of $(n,k,d)$ values, no helper selection scheme can ever improve the S-B tradeoff, and for the $(n,k,d)$ not in that subset, a new scheme called family helper selection (FHS) can strictly improve the S-B tradeoff over a blind helper selection scheme. Nonetheless, the analysis of FHS is done by a min-cut analysis with no actual code construction. This work fills this gap between pure min-cut analysis and actual code construction by pairing FHS with a new, generalized version of the existing fractional repetition (FR) codes. Specifically, existing FR codes are exact-repair codes that admit the highly-desirable repair-by-transfer property, but its unique construction limits the application to a restricted set of $(n,k,d)$ values. In contrast, our new construction, termed flexible fractional repetition codes, can be applied to arbitrary $(n,k,d)$ while retaining most of the practical benefits of FR codes, i.e., admitting small repair bandwidth, being exact-repair, and being almost repairable-by-transfer.

cs.IT↗

arXiv2016

Robust And Optimal Opportunistic Scheduling For Downlink 2-Flow Network Coding With Varying Channel Quality and Rate Adaptation (New Simulation Figures)

This paper considers the downlink traffic from a base station to two different clients. When assuming infinite backlog, it is known that inter-session network coding (INC) can significantly increase the throughput. However, the corresponding scheduling solution (when assuming dynamic arrivals instead and requiring bounded delay) is still nascent. For the 2-flow downlink scenario, we propose the first opportunistic INC + scheduling solution that is provably optimal for time-varying channels, i.e., the corresponding stability region matches the optimal Shannon capacity. Specifically, we first introduce a new binary INC operation, which is distinctly different from the traditional wisdom of XORing two overheard packets. We then develop a queue-length-based scheduling scheme and prove that it, with the help of the new INC operation, achieves the optimal stability region with time-varying channel quality. The proposed algorithm is later generalized to include the capability of rate adaptation. Simulation results show that it again achieves the optimal throughput with rate adaptation. A byproduct of our results is a scheduling scheme for stochastic processing networks (SPNs) with random departure, which relaxes the of deterministic departure in the existing results.

cs.NI↗

arXiv2016

Locally Repairable Regenerating Codes: Node Unavailability and the Insufficiency of Stationary Local Repair

Locally repairable codes (LRCs) are ingeniously designed distributed storage codes with a (usually small) fixed set of helper nodes participating in repair. Since most existing LRCs assume exact repair and allow full exchange of the stored data ($β=α$) from the helper nodes, they can be viewed as a generalization of the traditional erasure codes (ECs) with a much desired feature of local repairability via predetermined sets of helpers. However, it also means that they lack the features of (i) functional repair, and (ii) partial information-exchange ($β<α$) in the original regenerating codes (RCs), which could further reduce the repair bandwidth. Motivated by the significant bandwidth reduction of RCs over ECs, existing works by Ahmad et al and by Hollmann studied the concept of "locally repairable regenerating codes (LRRCs)" that successfully combine functional repair and partial information exchange of regenerating codes with the much-desired local repairability feature of LRC. The resulting LRRCs demonstrate significant bandwidth reduction. One important issue that needs to be addressed by any local repair schemes (including both LRCs and LRRCs) is that sometimes designated helper nodes may be temporarily unavailable, the result of multiple failures, degraded reads, or other network dynamics. Under the setting of LRRCs with temporary node unavailability, this work studies the impact of different helper selection methods. It proves that with node unavailability, all existing methods of helper selection, including those used in RCs and LRCs, can be insufficient in terms of achieving the optimal repair-bandwidth. For some scenarios, it is necessary to combine LRRCs with a new helper selection method, termed dynamic helper selection, to achieve optimal repair bandwidth. This work also compares the performance of different helper selection methods and answers...

cs.IT↗

arXiv2016

Locally Repairable Regenerating Code Constructions

In this work, we give locally repairable regenerating code (LRRC) [1]-[3], [5], [6] constructions that can protect the file size promised by the graph analysis of the modified family helper selection (MFHS) scheme [1] at the minimum-bandwidth-regenerating (MBR) point.

cs.IT↗

arXiv2016

Linear Network Coding Capacity Region of The Smart Repeater with Broadcast Erasure Channels

This work considers the smart repeater network where a single source $s$ wants to send two independent packet streams to destinations $\{d_1,d_2\}$ with the help of relay $r$. The transmission from $s$ or $r$ is modeled by packet erasure channels: For each time slot, a packet transmitted by $s$ may be received, with some probabilities, by a random subset of $\{d_1,d_2,r\}$; and those transmitted by $r$ will be received by a random subset of $\{d_1,d_2\}$. Interference is avoided by allowing at most one of $\{s,r\}$ to transmit in each time slot. One example of this model is any cellular network that supports two cell-edge users when a relay in the middle uses the same downlink resources for throughput/safety enhancement. In this setting, we study the capacity region of $(R_1,R_2)$ when allowing linear network coding (LNC). The proposed LNC inner bound introduces more advanced packing-mixing operations other than the previously well-known butterfly-style XOR operation on overheard packets of two co-existing flows. A new LNC outer bound is derived by exploring the inherent algebraic structure of the LNC problem. Numerical results show that, with more than 85% of the experiments, the relative sum-rate gap between the proposed outer and inner bounds is smaller than 0.08% under the strong-relaying setting and 0.04% under arbitrary distributions, thus effectively bracketing the LNC capacity of the smart repeater problem.

cs.IT↗

arXiv2016

When Can Helper Node Selection Improve Regenerating Codes? Part I: Graph-Based Analysis

Regenerating codes (RCs) can significantly reduce the repair-bandwidth of distributed storage networks. Initially, the analysis of RCs was based on the assumption that during the repair process, the newcomer does not distinguish (among all surviving nodes) which nodes to access, i.e., the newcomer is oblivious to the set of helpers being used. Such a scheme is termed the blind helper selection (BHS) scheme. Nonetheless, it is intuitive in practice that the newcomer should choose to access only those "good" helpers. In this two-part paper, a new characterization of the effect of choosing the helper nodes in terms of the storage-bandwidth tradeoff is given. Specifically, the answer to the following fundamental question is provided: Under what condition does proactively choosing the helper nodes improve the storage-bandwidth tradeoff? Through a graph-based analysis, this Part I paper answers this question by providing a necessary and sufficient condition under which optimally choosing good helpers strictly improves the storage-bandwidth tradeoff. A low-complexity helper selection solution, termed the family helper selection (FHS) scheme, is proposed and the corresponding storage/repair-bandwidth curve is characterized. This Part I paper also proves that under some design parameters, the FHS scheme is indeed optimal among all helper selection schemes. In the Part II paper, an explicit construction of an exact-repair code is proposed that achieves the minimum-bandwidth-regenerating (MBR) point of the FHS scheme. The new exact-repair code can be viewed as a generalization of the existing fractional repetition code.

cs.IT↗

arXiv2015

The two-unicast problem

We consider the communication capacity of wireline networks for a two-unicast traffic pattern. The network has two sources and two destinations with each source communicating a message to its own destination, subject to the capacity constraints on the directed edges of the network. We propose a simple outer bound for the problem that we call the Generalized Network Sharing (GNS) bound. We show this bound is the tightest edge-cut bound for two-unicast networks and is tight in several bottleneck cases, though it is not tight in general. We also show that the problem of computing the GNS bound is NP-complete. Finally, we show that despite its seeming simplicity, the two-unicast problem is as hard as the most general network coding problem. As a consequence, linear coding is insufficient to achieve capacity for general two-unicast networks, and non-Shannon inequalities are necessary for characterizing capacity of general two-unicast networks.

cs.IT↗

arXiv2014

Robust And Optimal Opportunistic Scheduling For Downlink 2-Flow Network Coding With Varying Channel Quality and Rate Adaptation

This paper considers the downlink traffic from a base station to two different clients. When assuming infinite backlog, it is known that inter-session network coding (INC) can significantly increase the throughput of each flow. However, the corresponding scheduling solution (when assuming dynamic arrivals instead and requiring bounded delay) is still nascent. For the 2-flow downlink scenario, we propose the first opportunistic INC + scheduling solution that is provably optimal for time-varying channels, i.e., the corresponding stability region matches the optimal Shannon capacity. Specifically, we first introduce a new binary INC operation, which is distinctly different from the traditional wisdom of XORing two overheard packets. We then develop a queue-length-based scheduling scheme, which, with the help of the new INC operation, can robustly and optimally adapt to time-varying channel quality. We then show that the proposed algorithm can be easily extended for rate adaptation and it again robustly achieves the optimal throughput. A byproduct of our results is a scheduling scheme for stochastic processing networks (SPNs) with random departure, which relaxes the assumption of deterministic departure in the existing results. The new SPN scheduler could thus further broaden the applications of SPN scheduling to other real-world scenarios.

cs.NI↗

arXiv2014

When and By How Much Can Helper Node Selection Improve Regenerating Codes?

Regenerating codes (RCs) can significantly reduce the repair-bandwidth of distributed storage networks. Initially, the analysis of RCs was based on the assumption that during the repair process, the newcomer does not distinguish (among all surviving nodes) which nodes to access, i.e., the newcomer is oblivious to the set of helpers being used. Such a scheme is termed the blind repair (BR) scheme. Nonetheless, it is intuitive in practice that the newcomer should choose to access only those "good" helpers. In this paper, a new characterization of the effect of choosing the helper nodes in terms of the storage-bandwidth tradeoff is given. Specifically, answers to the following fundamental questions are given: Under what conditions does proactively choosing the helper nodes improve the storage-bandwidth tradeoff? Can this improvement be analytically quantified? This paper answers the former question by providing a necessary and sufficient condition under which optimally choosing good helpers strictly improves the storage-bandwidth tradeoff. To answer the latter question, a low-complexity helper selection solution, termed the family repair (FR) scheme, is proposed and the corresponding storage/repair-bandwidth curve is characterized. For example, consider a distributed storage network with 60 total number of nodes and the network is resilient against 50 node failures. If the number of helper nodes is 10, then the FR scheme and its variant demonstrate 27% reduction in the repair-bandwidth when compared to the BR solution. This paper also proves that under some design parameters, the FR scheme is indeed optimal among all helper selection schemes. An explicit construction of an exact-repair code is also proposed that can achieve the minimum-bandwidth-regenerating point of the FR scheme. The new exact-repair code can be viewed as a generalization of the existing fractional repetition code.

cs.IT↗