On Deep Holes of Projective Reed-Solomon Codes
In this paper, we obtain new results on the covering radius and deep holes for projective Reed-Solomon (PRS) codes.
cs.IT↗
arXiv subjects
Jun Zhang
Publications and source records attributed to Jun Zhang.
Schedule path optimization for quantum annealing and adiabatic quantum computing
Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are probabilistic in nature and the minimum gap between the ground state and first excited state of the system during evolution is a major factor in determining the success probability. In this work we investigate a strategy for increasing the minimum gap and success probability by introducing intermediate Hamiltonians that modify the evolution path between initial and final Hamiltonians. We focus on an optimization problem relevant to recent hardware implementations and present numerical evidence for the existence of a purely local intermediate Hamiltonian that achieve the optimum performance in terms of pushing the minimum gap to one of the end points of the evolution. As a part of this study we develop a convex optimization formulation of the search for optimal adiabatic schedules that makes this computation more tractable, and which may be of independent interest. We further study the effectiveness of random intermediate Hamiltonians on the minimum gap and success probability, and empirically find that random Hamiltonians have a significant probability of increasing the success probability, but only by a modest amount.
quant-ph↗
Energy Efficient Downlink Transmission for Multi-cell Massive DAS with Pilot Contamination
In this paper, we study the energy efficiency (EE) of a downlink multi-cell massive distributed antenna system (DAS) in the presence of pilot contamination (PC), where the antennas are clustered on the remote radio heads (RRHs). We employ a practical power consumption model by considering the transmit power, the circuit power, and the backhaul power, in contrast to most of the existing works which focus on co-located antenna systems (CAS) where the backhaul power is negligible. For a given average user rate, we consider the problem of maximizing the EE with respect to the number of each RRH antennas $n$, the number of RRHs $M$, the number of users $K$, and study the impact of system parameters on the optimal $n$, $M$ and $K$. Specifically, by applying random matrix theory, we derive the closed-form expressions of the optimal $n$, and find the solution of the optimal $M$ and $K$, under a simplified channel model with maximum ratio transmission. From the results, we find that to achieve the optimal EE, a large number of antennas is needed for a given user rate and PC. As the number of users increases, EE can be improved further by having more RRHs and antennas. Moreover, if the backhauling power is not large, massive DAS can be more energy efficient than massive CAS. These insights provide a useful guide to practical deployment of massive DAS.
cs.IT↗
Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms
Given a symplectic surface $(Σ, ω)$ of genus $g \ge 4$, we show that the free group with two generators embeds into every asymptotic cone of $(\mathrm{Ham}(Σ, ω), d_\mathrm{H})$, where $d_\mathrm{H}$ is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.
math.SG↗
Photon statistics on the extreme entanglement
The effects of photon bunching and antibunching correspond to the classical and quantum features of the electromagnetic field, respectively. No direct evidence suggests whether these effects can be potentially related to quantum entanglement. Here we design a cavity quantum electrodynamics model with two atoms trapped in to demonstrate the connections between the steady-state photon statistics and the two-atom entanglement . It is found that within the weak dissipations and to some good approximation, the local maximal two-atom entanglements perfectly correspond to not only the quantum feature of the electromagnetic field---the optimal photon antibunching, but also the classical feature---the optimal photon bunching. We also analyze the influence of strong dissipations and pure dephasing. An intuitive physical understanding is also given finally.
quant-ph↗
Periodically modulated electromagnetically induced transparency
Phenomena of electromagnetically induced transparency (PEIT) may be interpreted by the Autler-Townes Splitting (ATS), where the coupled states are split by the coupling laser field, or by the quantum destructive interference (QDI), where the atomic phases caused by the coupling laser and the probe laser field cancel. We propose modulated experiments to explore the PEIT in an alternative way by periodically modulating the coupling and the probe fields in a ?-type three-level system. Our analytical and numerical results rule out the ATS interpretation and show that the QDI interpretation is more appropriate for the modulated experiments. The proposed experiments are readily implemented in atomic gases, artificial atoms in superconducting quantum devices, or three-level meta-atoms in meta-materials.
quant-ph↗
Trace and determinant preserving maps of matrices
Suppose a map $ϕ$ on the set of positive definite matrices satisfies $\det(A+B)=\det(ϕ(A)+ϕ(B))$. Then we have $${\rm tr}(AB^{-1}) = {\rm tr}(ϕ(A){ϕ(B)}^{-1}).$$ Through this viewpoint, we show that $ϕ$ is of the form $ϕ(A)= M^*AM$ or $ϕ(A)= M^*A^tM$ for some invertible matrix $M$ with $\det (M^*M)=1$. We also characterize the map $ϕ: \mathcal{S} \rightarrow \mathcal{S}$ preserving the determinant of convex combinations in $\mathcal{S}$ by using similar method. Here $\mathcal{S}$ can be the set of complex matrices, positive definite matrices, symmetric matrices, and upper triangular matrices.
math.RA↗
Subarcsecond Bright Points and Quasi-periodic Upflows Below a Quiescent Filament Observed by the IRIS
Using UV spectra and SJIs from the IRIS, and coronal images and magnetograms from the Solar Dynamics Observatory (SDO), we present the new features in a quiescent filament channel: subarcsecond bright points (BPs) and quasi-periodic upflows. The BPs in the TR have a spatial scale of about 350$-$580 km and lifetime of more than several tens of minutes. They are located at stronger magnetic structures in the filament channel, with magnetic flux of about 10$^{17}$$-$10$^{18}$ Mx. Quasi-periodic brightenings and upflows are observed in the BPs and the period is about 4$-$5 min. The BP and the associated jet-like upflow comprise a "tadpole-shaped" structure. The upflows move along bright filament threads and their directions are almost parallel to the spine of the filament. The upflows initiated from the BPs with opposite polarity magnetic fields have opposite directions. The velocity of the upflows in plane of sky is about 5$-$50 km s$^{-1}$. The emission line of Si IV 1402.77 Å at the locations of upflows exhibits obvious blueshifts of about 5$-$30 km s$^{-1}$, and the line profile is broadened with the width of more than 20 km s$^{-1}$. The BPs seem to be the bases of filament threads and the upflows are able to convey mass for the dynamic balance of the filament. The "counter-streaming" flows in previous observations may be caused by the propagation of bi-directional upflows initiated from opposite polarity magnetic fields. We suggest that quasi-periodic brightenings of BPs and quasi-periodic upflows result from small-scale oscillatory magnetic reconnections, which are modulated by solar p-mode waves.
astro-ph.SR↗
Low-Rank Matrix Completion for Topological Interference Management by Riemannian Pursuit
In this paper, we present a flexible low-rank matrix completion (LRMC) approach for topological interference management (TIM) in the partially connected K-user interference channel. No channel state information (CSI) is required at the transmitters except the network topology information. The previous attempt on the TIM problem is mainly based on its equivalence to the index coding problem, but so far only a few index coding problems have been solved. In contrast, in this paper, we present an algorithmic approach to investigate the achievable degrees-of-freedom (DoFs) by recasting the TIM problem as an LRMC problem. Unfortunately, the resulting LRMC problem is known to be NP-hard, and the main contribution of this paper is to propose a Riemannian pursuit (RP) framework to detect the rank of the matrix to be recovered by iteratively increasing the rank. This algorithm solves a sequence of fixed-rank matrix completion problems. To address the convergence issues in the existing fixed-rank optimization methods, the quotient manifold geometry of the search space of fixed-rank matrices is exploited via Riemannian optimization. By further exploiting the structure of the low-rank matrix varieties, i.e., the closure of the set of fixed- rank matrices, we develop an efficient rank increasing strategy to find good initial points in the procedure of rank pursuit. Simulation results demonstrate that the proposed RP algorithm achieves a faster convergence rate and higher achievable DoFs for the TIM problem compared with the state-of-the-art methods.
cs.IT↗
QoS-Aware Joint Mode Selection and Channel Assignment for D2D Communications
Underlaying device-to-device (D2D) communications to a cellular network is considered as a key technique to improve spectral efficiency in 5G networks. For such D2D systems, mode selection and resource allocation have been widely utilized for managing interference. However, previous works allowed at most one D2D link to access the same channel, while mode selection and resource allocation are typically separately designed. In this paper, we jointly optimize the mode selection and channel assignment in a cellular network with underlaying D2D communications, where multiple D2D links may share the same channel. Meanwhile, the QoS requirements for both cellular and D2D links are guaranteed, in terms of Signal-to-Interference-plus-Noise Ratio (SINR). We first propose an optimal dynamic programming (DP) algorithm, which provides a much lower computation complexity compared to exhaustive search and serves as the performance bench mark. A bipartite graph based greedy algorithm is then proposed to achieve a polynomial time complexity. Simulation results will demonstrate the advantage of allowing each channel to be accessed by multiple D2D links in dense D2D networks, as well as, the effectiveness of the proposed algorithms.
cs.IT↗
Selective Uplink Training for Massive MIMO Systems
As a promising technique to meet the drastically growing demand for both high throughput and uniform coverage in the fifth generation (5G) wireless networks, massive multiple-input multiple-output (MIMO) systems have attracted significant attention in recent years. However, in massive MIMO systems, as the density of mobile users (MUs) increases, conventional uplink training methods will incur prohibitively high training overhead, which is proportional to the number of MUs. In this paper, we propose a selective uplink training method for massive MIMO systems, where in each channel block only part of the MUs will send uplink pilots for channel training, and the channel states of the remaining MUs are predicted from the estimates in previous blocks, taking advantage of the channels' temporal correlation. We propose an efficient algorithm to dynamically select the MUs to be trained within each block and determine the optimal uplink training length. Simulation results show that the proposed training method provides significant throughput gains compared to the existing methods, while much lower estimation complexity is achieved. It is observed that the throughput gain becomes higher as the MU density increases.
cs.IT↗
Cache Size Allocation in Backhaul Limited Wireless Networks
Caching popular content at base stations is a powerful supplement to existing limited backhaul links for accommodating the exponentially increasing mobile data traffic. Given the limited cache budget, we investigate the cache size allocation problem in cellular networks to maximize the user success probability (USP), taking wireless channel statistics, backhaul capacities and file popularity distributions into consideration. The USP is defined as the probability that one user can successfully download its requested file either from the local cache or via the backhaul link. We first consider a single-cell scenario and derive a closed-form expression for the USP, which helps reveal the impacts of various parameters, such as the file popularity distribution. More specifically, for a highly concentrated file popularity distribution, the required cache size is independent of the total number of files, while for a less concentrated file popularity distribution, the required cache size is in linear relation to the total number of files. Furthermore, we study the multi-cell scenario, and provide a bisection search algorithm to find the optimal cache size allocation. The optimal cache size allocation is verified by simulations, and it is shown to play a more significant role when the file popularity distribution is less concentrated.
cs.IT↗
Black holes and the multiverse
Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive black holes. The mechanism of black hole formation described in this paper is very generic and has important implications for the global structure of the universe. Baby universes inside super-critical black holes inflate eternally and nucleate bubbles of all vacua allowed by the underlying particle physics. The resulting multiverse has a very non-trivial spacetime structure, with a multitude of eternally inflating regions connected by wormholes. If a black hole population with the predicted mass spectrum is discovered, it could be regarded as evidence for inflation and for the existence of a multiverse.
hep-th↗
ARQ with Adaptive Feedback for Energy Harvesting Receivers
Automatic repeat request (ARQ) is widely used in modern communication systems to improve transmission reliability. In conventional ARQ protocols developed for systems with energy-unconstrained receivers, an acknowledgement/negative-acknowledgement (ACK/NACK) message is fed back when decoding succeeds/fails. Such kind of non-adaptive feedback consumes significant amount of energy, and thus will limit the performance of systems with energy harvesting (EH) receivers. In order to overcome this limitation and to utilize the harvested energy more efficiently, we propose a novel ARQ protocol for EH receivers, where the ACK feedback can be adapted based upon the receiver's EH state. Two conventional ARQ protocols are also considered. By adopting the packet drop probability (PDP) as the performance metric, we formulate the throughput constrained PDP minimization problem for a communication link with a non-EH transmitter and an EH receiver. Optimal reception policies including the sampling, decoding and feedback strategies, are developed for different ARQ protocols. Simulation results will show that the proposed ARQ protocol not only outperforms the conventional ARQs in terms of PDP, but can also achieve a higher throughput.
cs.IT↗
Success Probability and Area Spectral Efficiency in Multiuser MIMO HetNets
We derive a general and closed-form result for the success probability in downlink multiple-antenna (MIMO) heterogeneous cellular networks (HetNets), utilizing a novel Toeplitz matrix representation. This main result, which is equivalently the signal-to-interference ratio (SIR) distribution, includes multiuser MIMO, single-user MIMO and per-tier biasing for $K$ different tiers of randomly placed base stations (BSs), assuming zero-forcing precoding and perfect channel state information. The large SIR limit of this result admits a simple closed form that is accurate at moderate SIRs, e.g., above 5 dB. These results reveal that the SIR-invariance property of SISO HetNets does not hold for MIMO HetNets; instead the success probability may decrease as the network density increases. We prove that the maximum success probability is achieved by activating only one tier of BSs, while the maximum area spectral efficiency (ASE) is achieved by activating all the BSs. This reveals a unique tradeoff between the ASE and link reliability in multiuser MIMO HetNets. To achieve the maximum ASE while guaranteeing a certain link reliability, we develop efficient algorithms to find the optimal BS densities. It is shown that as the link reliability requirement increases, more BSs and more tiers should be deactivated.
cs.IT↗
Tether-cutting Reconnection between Two Solar Filaments Triggering Outflows and a Coronal Mass Ejection
Triggering mechanisms of solar eruptions have long been a challenge. A few previous case studies have indicated that preceding gentle filament merging via magnetic reconnection may launch following intense eruption, according with the tether-cutting (TC) model. However, detailed process of TC reconnection between filaments has not been exhibited yet. In this work, we report the high resolution observations from the Interface Region Imaging Spectrometer (IRIS) of TC reconnection between two sheared filaments in NOAA active region 12146. The TC reconnection commenced since 15:35 UT on 2014 August 29 and triggered an eruptive GOES C4.3-class flare 8 minutes later. An associated coronal mass ejection appeared in the field of view of SOHO/LASCO C2 about 40 minutes later. Thanks to the high spatial resolution of IRIS data, bright plasma outflows generated by the TC reconnection are clearly observed, which moved along the subarcsecond fine-scale flux tube structures in the erupting filament. Based on the imaging and spectral observations, the mean plane-of-sky and line-of-sight velocities of the TC reconnection outflows are separately measured to be 79 and 86 km/s, which derives an average real speed of 120 km/s. In addition, it is found that spectral features, such as peak intensities, Doppler shifts, and line widths in the TC reconnection region evidently enhanced compared with those in the nearby region just before the flare.
astro-ph.SR↗
Grid Energy Consumption and QoS Tradeoff in Hybrid Energy Supply Wireless Networks
Hybrid energy supply (HES) wireless networks have recently emerged as a new paradigm to enable green networks, which are powered by both the electric grid and harvested renewable energy. In this paper, we will investigate two critical but conflicting design objectives of HES networks, i.e., the grid energy consumption and quality of service (QoS). Minimizing grid energy consumption by utilizing the harvested energy will make the network environmentally friendly, but the achievable QoS may be degraded due to the intermittent nature of energy harvesting. To investigate the tradeoff between these two aspects, we introduce the total service cost as the performance metric, which is the weighted sum of the grid energy cost and the QoS degradation cost. Base station assignment and power control is adopted as the main strategy to minimize the total service cost, while both cases with non-causal and causal side information are considered. With non-causal side information, a Greedy Assignment algorithm with low complexity and near-optimal performance is proposed. With causal side information, the design problem is formulated as a discrete Markov decision problem. Interesting solution structures are derived, which shall help to develop an efficient monotone backward induction algorithm. To further reduce complexity, a Look-Ahead policy and a Threshold-based Heuristic policy are also proposed. Simulation results shall validate the effectiveness of the proposed algorithms and demonstrate the unique grid energy consumption and QoS tradeoff in HES networks.
cs.IT↗
Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems
Millimeter wave (mmWave) communications has been regarded as a key enabling technology for 5G networks. In contrast to conventional multiple-input-multiple-output (MIMO) systems, precoding in mmWave MIMO cannot be performed entirely at baseband using digital precoders, as only a limited number of signal mixers and analog-to-digital converters (ADCs) can be supported considering their cost and power consumption. As a cost-effective alternative, a hybrid precoding transceiver architecture, combining a digital precoder and an analog precoder, has recently received considerable attention. However, the optimal design of such hybrid precoders has not been fully understood. In this paper, treating the hybrid precoder design as a matrix factorization problem, effective alternating minimization (AltMin) algorithms will be proposed for two different hybrid precoding structures, i.e., the fully-connected and partially-connected structures. In particular, for the fully-connected structure, an AltMin algorithm based on manifold optimization is proposed to approach the performance of the fully digital precoder, which, however, has a high complexity. Thus, a low-complexity AltMin algorithm is then proposed, by enforcing an orthogonal constraint on the digital precoder. Furthermore, for the partially-connected structure, an AltMin algorithm is also developed with the help of semidefinite relaxation. For practical implementation, the proposed AltMin algorithms are further extended to the broadband setting with orthogonal frequency division multiplexing (OFDM) modulation. Simulation results will demonstrate significant performance gains of the proposed AltMin algorithms over existing hybrid precoding algorithms. Moreover, based on the proposed algorithms, simulation comparisons between the two hybrid precoding structures will provide valuable design insights.
cs.IT↗