arXiv subjects

Jian Song

Publications and source records attributed to Jian Song.

At least 163 records · Page 9Linked to original sources

arXiv2020

Binary Neural Network Aided CSI Feedback in Massive MIMO System

In massive multiple-input multiple-output (MIMO) system, channel state information (CSI) is essential for the base station to achieve high performance gain. Recently, deep learning is widely used in CSI compression to fight against the growing feedback overhead brought by massive MIMO in frequency division duplexing system. However, applying neural network brings extra memory and computation cost, which is non-negligible especially for the resource limited user equipment (UE). In this paper, a novel binarization aided feedback network named BCsiNet is introduced. Moreover, BCsiNet variants are designed to boost the performance under customized training and inference schemes. Experiments shows that BCsiNet offers over 30$\times$ memory saving and around 2$\times$ inference acceleration for encoder at UE compared with CsiNet. Furthermore, the feedback performance of BCsiNet is comparable with original CsiNet. The key results can be reproduced with https://github.com/Kylin9511/BCsiNet.

cs.IT↗

arXiv2020

Metric rigidity of Kahler manifolds with lower Ricci bounds and almost maximal volume

In this short note we prove that a Kahler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results of Kewei Zhang and Yuchen Liu on holomorphic rigidity of such Kahler manifolds with the structure theorem of Tian-Wang for almost Einstein manifolds. This can be regarded as the complex analog of the result on Colding on the shape of Riemannian manifolds with almost maximal volume

math.DG↗

arXiv2020

An Analytic Proof of the Stable Reduction Theorem

The stable reduction theorem says that a family of curves of genus $g\geq 2$ over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new proof of this result for curves defined over $\mathbb{C}$ using the Kähler-Einstein metrics on the fibers to obtain the limiting stable curves at the punctures.

math.DG↗

arXiv2020

Continuity of the Weil-Petersson potential

Let $\mathcal{M}_{\rm KSB}$ (resp. $\mathcal{M}_{\rm KSB}'$) be the the moduli space of $n$-dimensional Kähler-Einstein manifolds (resp. varieties) $X$ with $K_X$ ample. We prove that the Weil-Petersson metric on $\mathcal{M}_{\rm KSB}$ extends uniquely to the projective variety $\mathcal{M}_{\rm KSB}'$, as a closed positive current with continuous local potentials. This generalizes a theorem of Wolpert which treats the case $n=1$, and also confirms a conjecture of Berman-Guenancia. In addition, we derive uniform estimates for the volumes of sublevel sets of Kähler-Einstein potentials

math.DG↗

arXiv2020

Eigenvalue distributions of high-dimensional matrix processes driven by fractional Brownian motion

In this article, we study high-dimensional behavior of empirical spectral distributions $\{L_N(t), t\in[0,T]\}$ for a class of $N\times N$ symmetric/Hermitian random matrices, whose entries are generated from the solution of stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H \in(1/2,1)$. For Wigner-type matrices, we obtain almost sure relative compactness of $\{L_N(t), t\in[0,T]\}_{N\in\mathbb N}$ in $C([0,T], \mathbf P(\mathbb R))$ following the approach in \cite{Anderson2010}; for Wishart-type matrices, we obtain tightness of $\{L_N(t), t\in[0,T]\}_{N\in\mathbb N}$ on $C([0,T], \mathbf P(\mathbb R))$ by tightness criterions provided in Appendix \ref{subset:tightness argument}. The limit of $\{L_N(t), t\in[0,T]\}$ as $N\to \infty$ is also characterised.

math.PR↗

arXiv2020

Extensions of the I-MMSE Relationship to Gaussian Channels with Feedback and Memory

Unveiling a fundamental link between information theory and estimation theory, the I-MMSE relationship by Guo, Shamai and Verdu~\cite{gu05}, together with its numerous extensions, has great theoretical significance and various practical applications. On the other hand, its influences to date have been restricted to channels without feedback or memory, due to the absence of its extensions to such channels. In this paper, we propose extensions of the I-MMSE relationship to discrete-time and continuous-time Gaussian channels with feedback and/or memory. Our approach is based on a very simple observation, which can be applied to other scenarios, such as a simple and direct proof of the classical de Bruijn's identity. This submission corrects the mistakes in the previous version.

cs.IT↗

arXiv2020

On collision of multiple eigenvalues for matrix-valued Gaussian processes

For real symmetric and complex Hermitian Gaussian processes whose values are $d\times d$ matrices, we characterize the conditions under which the probability that at least $k$ eigenvalues collide is positive for $2\le k\le d$, and we obtain the Hausdorff dimension of the set of collision times.

math.PR↗

arXiv2020

Minimizing Age of Information with Power Constraints: Multi-user Opportunistic Scheduling in Multi-State Time-Varying Channels

This work is motivated by the need of collecting fresh data from power-constrained sensors in the industrial Internet of Things (IIoT) network. A recently proposed metric, the Age of Information (AoI) is adopted to measure data freshness from the perspective of the central controller in the IIoT network. We wonder what is the minimum average AoI the network can achieve and how to design scheduling algorithms to approach it. To answer these questions when the channel states of the network are Markov time-varying and scheduling decisions are restricted to bandwidth constraint, we first decouple the multi-sensor scheduling problem into a single-sensor constrained Markov decision process (CMDP) through relaxation of the hard bandwidth constraint. Next we exploit the threshold structure of the optimal policy for the decoupled single sensor CMDP and obtain the optimum solution through linear programming (LP). Finally, an asymptotically optimal truncated policy that can satisfy the hard bandwidth constraint is built upon the optimal solution to each of the decoupled single-sensor. Our investigation shows that to obtain a small AoI performance: (1) The scheduler exploits good channels to schedule sensors supported by limited power; (2) Sensors equipped with enough transmission power are updated in a timely manner such that the bandwidth constraint can be satisfied.

cs.IT↗

arXiv2020

Riemannian geometry of Kahler-Einstein currents III: compactness of Kahler-Einstein manifolds of negative scalar curvature

Let $\mathcal{K}(n, V)$ be the set of $n$-dimensional compact Kahler-Einstein manifolds $(X, g)$ satisfying $Ric(g)= - g$ with volume bounded above by $V$. We prove that after passing to a subsequence, any sequence $\{ (X_j, g_j)\}_{j=1}^\infty$ in $\mathcal{K}(n, V)$ converges, in the pointed Gromov-Hausdorff topology, to a finite union of complete Kahler-Einstein metric spaces without loss of volume. The convergence is smooth off a closed singular set of Hausdorff dimension no greater than $2n-4$, and the limiting metric space is biholomorphic to an $n$-dimensional semi-log canonical model with its non log terminal locus of complex dimension no greater than $n-1$ removed. We also show that the Weil-Petersson metric extends uniquely to a Kahler current with bounded local potentials on the KSBA compactification of the moduli space of canonically polarized manifolds. In particular, the coarse KSBA moduli space has finite volume with respect to the Weil-Petersson metric. Our results are a high dimensional generalization of the well known compactness results for hyperbolic metrics on compact Riemann surfaces of fixed genus greater than one.

math.DG↗

arXiv2020

Scheduling to Minimize Age of Synchronization in Wireless Broadcast Networks with Random Updates

In this work, a wireless broadcast network with a base station (BS) sending random time-sensitive information updates to multiple users with interference constraints is considered. The Age of Synchronization (AoS), namely the amount of time elapsed since the information stored at the network user becomes desynchronized, is adopted to measure data freshness from the perspective of network users. Compared with the more widely used metric---the Age of Information (AoI), AoS accounts for the freshness of the randomly changing content. The AoS minimization scheduling problem is formulated into a discrete time Markov decision process and the optimal solution is approximated through structural finite state policy iteration. An index based heuristic scheduling policy based on restless multi-arm bandit (RMAB) is provided to further reduce computational complexity. Simulation results show that the proposed index policy can achieve compatible performance with the MDP and close to the AoS lower bound. Moreover, theoretic analysis and simulations reveal the differences between AoS and AoI. AoI minimization scheduling policy cannot guarantee a good AoS performance.

cs.IT↗

arXiv2019

Entropy flow and De Bruijn's identity for a class of stochastic differential equations driven by fractional Brownian motion

Motivated by the classical De Bruijn's identity for the additive Gaussian noise channel, in this paper we consider a generalized setting where the channel is modelled via stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in(0,1)$. We derive generalized De Bruijn's identity for Shannon entropy and Kullback-Leibler divergence by means of Itô's formula, and present two applications. In the first application we demonstrate its equivalence with Stein's identity for Gaussian distributions, while in the second application, we show that for $H \in (0,1/2]$, the entropy power is concave in time while for $H \in (1/2,1)$ it is convex in time when the initial distribution is Gaussian. Compared with the classical case of $H = 1/2$, the time parameter plays an interesting and significant role in the analysis of these quantities.

math.PR↗

arXiv2019

Scheduling to Minimize Age of Information in Multi-State Time-Varying Networks with Power Constraints

In this paper, we study how to collect fresh data in time-varying networks with power constrained users. We measure data freshness from the perspective of the central controller by using the metric Age of Information, namely the time elapsed since the generation time-stamp of the freshest information. We wonder what is the minimum AoI performance the network can achieve and how to design scheduling algorithms to approach it. To answer these questions when scheduling decisions are restricted to bandwidth constraint, we first decouple the multi-user scheduling problem into a single user constrained Markov decision process (CMDP) through relaxation of the hard bandwidth constraint. Next we exploit the threshold structure of the optimal policy for the decoupled single user CMDP and obtain the optimum solution through linear programming (LP). Finally, an asymptotic optimal truncated policy that can satisfy the hard bandwidth constraint is built upon the optimal solution to each of the decoupled single-user sub-problem. The performance is verified through simulations. Our investigation shows that to obtain a small AoI performance, the scheduler exploits good channels to schedule users supported by limited power. Users equipped with enough transmission power are updated in a timely manner such that the bandwidth constraint can be satisfied.

cs.IT↗

arXiv2019

Optimizing Data Freshness in Time-Varying Wireless Networks with Imperfect Channel State

We consider a scenario where a base station (BS) attempts to collect fresh information from power constrained sensors over time-varying band-limited wireless channels. We characterize the data freshness through the recently proposed metric--the Age of Information. We consider a time-varying channel model with power adaptation. Unlike previous work, packet loss may happen due to imperfect channel estimation or decoding error. We propose an asymptotic optimal scheduling algorithm minimizing AoI performance and satisfying both bandwidth and power constraint in such networks. Numerical simulations show that the proposed policy outperforms the greedy one, and we observe that sensors with poor channels are scheduled at higher AoI in order to limit the packet loss.

cs.IT↗

arXiv2019

High-dimensional limits of eigenvalue distributions for general Wishart process

In this article, we obtain an equation for the high-dimensional limit measure of eigenvalues of generalized Wishart processes, and the results is extended to random particle systems that generalize SDEs of eigenvalues. We also introduce a new set of conditions on the coefficient matrices for the existence and uniqueness of a strong solution for the SDEs of eigenvalues. The equation of the limit measure is further discussed assuming self-similarity on the eigenvalues.

math.PR↗

arXiv2019

Deep Learning based Channel Estimation Algorithm over Time Selective Fading Channels

The research about deep learning application for physical layer has been received much attention in recent years. In this paper, we propose a Deep Learning (DL) based channel estimator under time varying Rayleigh fading channel. We build up, train and test the channel estimator using Neural Network (NN). The proposed DL-based estimator can dynamically track the channel status without any prior knowledge about the channel model and statistic characteristics. The simulation results show the proposed NN estimator has better Mean Square Error (MSE) performance compared with the traditional algorithms and some other DL-based architectures. Furthermore, the proposed DL-based estimator also shows its robustness with the different pilot densities.

eess.SP↗

arXiv2019

High-dimensional central limit theorems for eigenvalue distributions of generalized Wishart processes

We consider eigenvalues of generalized Wishart processes as well as particle systems, of which the empirical measures converge to deterministic measures as the dimension goes to infinity. In this paper, we obtain central limit theorems to characterize the fluctuations of the empirical measures around the limit measures by using stochastic calculus. As applications, central limit theorems for the Dyson's Brownian motion and the eigenvalues of the Wishart process are recovered under slightly more general initial conditions, and a central limit theorem for the eigenvalues of a symmetric Ornstein-Uhlenbeck matrix process is obtained.

math.PR↗

arXiv2019

The lubricity of mucin solutions is robust toward changes in physiological conditions

Solutions of manually purified gastric mucins have been shown to be promising lubricants for biomedical purposes, where they can efficiently reduce friction and wear. However, so far, such mucin solutions have been mostly tested in specific settings, and variations in the composition of the lubricating fluid have not been systematically explored. We here fill this gap and determine the viscosity, adsorption behavior, and lubricity of porcine gastric mucin solutions on hydrophobic surfaces at different pH levels, mucin and salt concentrations and in the presence of other proteins. We demonstrate that mucin solutions provide excellent lubricity even at very low concentrations of 0.01 % (w/v), over a broad range of pH levels and even at elevated ionic strength. Furthermore, we provide mechanistic insights into mucin lubricity, which help explain how certain variations in physiologically relevant parameters can limit the lubricating potential of mucin solutions. Our results motivate that solutions of manually purified mucin solutions can be powerful biomedical lubricants, e.g. serving as eye drops, mouth sprays or as a personal lubricant for intercourse.

q-bio.BM↗

arXiv2019

Fractional stochastic wave equation driven by a Gaussian noise rough in space

In this article, we consider fractional stochastic wave equations on $\mathbb R$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in(\frac14, \frac12)$ in space. We prove the existence and uniqueness of the mild Skorohod solution, establish lower and upper bounds for the $p$-th moment of the solution for all $p\ge2$, and obtain the Hölder continuity in time and space variables for the solution.

math.PR↗