arXiv subjects

Long Shi

Publications and source records attributed to Long Shi.

67 records · Page 4Linked to original sources

arXiv2019

Some new Constructions of Coded Caching Schemes with Reduced Subpacketization

We study the problem of constructing centralized coded caching schemes with low subpacketization level based on the placement delivery array (PDA) design framework. PDA design is an efficient way to construct centralized coded caching schemes and most existing schemes, including the famous Maddah-Ali-Niesen scheme, can be described using PDA. In this paper, we first prove that constructing a PDA is equivalent to constructing three binary matrices that satisfy certain conditions. From this perspective, we then propose some new constructions of coded caching schemes using PDA design based on projective geometries over finite fields, combinatorial configurations, and t-designs, respectively. Our constructions achieve low subpacketization level (e.g., linear subpacketization) with reasonable rate loss and include several known results as special cases. Finally, we give an approach to construct new coded caching scheme from existing schemes based on direct product of PDAs. Our results enrich the coded caching schemes of low subpacketization level.

cs.IT↗

arXiv2018

Information Theoretic Bounds Based Channel Quantization Design for Emerging Memories

Channel output quantization plays a vital role in high-speed emerging memories such as the spin-torque transfer magnetic random access memory (STT-MRAM), where high-precision analog-to-digital converters (ADCs) are not applicable. In this paper, we investigate the design of the 1-bit quantizer which is highly suitable for practical applications. We first propose a quantized channel model for STT-MRAM. We then analyze various information theoretic bounds for the quantized channel, including the channel capacity, cutoff rate, and the Polyanskiy-Poor-Verdú (PPV) finite-length performance bound. By using these channel measurements as criteria, we design and optimize the 1-bit quantizer numerically for the STT-MRAM channel. Simulation results show that the proposed quantizers significantly outperform the conventional minimum mean-squared error (MMSE) based Lloyd-Max quantizer, and can approach the performance of the 1-bit quantizer optimized by error rate simulations.

cs.IT↗

arXiv2018

Diffusion Leaky Zero Attracting Least Mean Square Algorithm and Its Performance Analysis

Recently, the leaky diffusion least-mean-square (DLMS) algorithm has obtained much attention because of its good performance for high input eigenvalue spread and low signal-to-noise ratio (SNR). However, the leaky DLMS algorithm may suffer from performance deterioration in the sparse system. To overcome this drawback, the leaky zero attracting DLMS (LZA-DLMS) algorithm is developed in this paper, which adds an l1-norm penalty to the cost function to exploit the property of sparse system. The leaky reweighted zero attracting DLMS (LRZA-DLMS) algorithm is also put forward, which can improve the estimation performance in the presence of time-varying sparsity. Instead of using the l1-norm penalty, in the reweighted version, a log-sum function is employed as the substitution. Based on the weight error variance relation and several common assumptions, we analyze the transient behavior of our findings and determine the stability bound of the step-size. Moreover, we implement the steady state theoretical analysis for the proposed algorithms. Simulations in the context of distributed network system identification illustrate that the proposed schemes outperform various existing algorithms and validate the accuracy of the theoretical results.

eess.SP↗

arXiv2018

The Role of Tensor Force in Heavy-Ion Fusion Dynamics

The tensor force is implemented into the time-dependent Hartree-Fock (TDHF) theory so that both exotic and stable collision partners, as well as their dynamics in heavy-ion fusion, can be described microscopically. The role of tensor force on fusion dynamics is systematically investigated for $^{40}\mathrm{Ca}+\mathrm{^{40}Ca}$, $^{40}\mathrm{Ca}+\mathrm{^{48}Ca}$, $^{48}\mathrm{Ca}+\mathrm{^{48}Ca}$, $^{48}\mathrm{Ca}+\mathrm{^{56}Ni}$, and $^{56}\mathrm{Ni}+\mathrm{^{56}Ni}$ reactions which vary by the total number of spin-unsaturated magic numbers in target and projectile. A notable effect on fusion barriers and cross sections is observed by the inclusion of tensor force. The origin of this effect is analyzed. The influence of isoscalar and isovector tensor terms is investigated with the T$IJ$ forces. These effects of tensor force in fusion dynamics are essentially attributed to the shift of low-lying vibration states of colliding partners and nucleon transfer in the asymmetric reactions. Our calculations of above-barrier fusion cross sections also show that tensor force does not significantly affect the dynamical dissipation at near-barrier energies.

nucl-th↗

arXiv2016

Complex Linear Physical-Layer Network Coding

This paper presents the results of a comprehensive investigation of complex linear physical-layer network (PNC) in two-way relay channels (TWRC). A critical question at relay R is as follows: "Given channel gain ratio $η= h_A/h_B$, where $h_A$ and $h_B$ are the complex channel gains from nodes A and B to relay R, respectively, what is the optimal coefficients $(α,β)$ that minimizes the symbol error rate (SER) of $w_N=αw_A+βw_B$ when we attempt to detect $w_N$ in the presence of noise?" Our contributions with respect to this question are as follows: (1) We put forth a general Gaussian-integer formulation for complex linear PNC in which $α,β,w_A, w_B$, and $w_N$ are elements of a finite field of Gaussian integers, that is, the field of $\mathbb{Z}[i]/q$ where $q$ is a Gaussian prime. Previous vector formulation, in which $w_A$, $w_B$, and $w_N$ were represented by $2$-dimensional vectors and $α$ and $β$ were represented by $2\times 2$ matrices, corresponds to a subcase of our Gaussian-integer formulation where $q$ is real prime only. Extension to Gaussian prime $q$, where $q$ can be complex, gives us a larger set of signal constellations to achieve different rates at different SNR. (2) We show how to divide the complex plane of $η$ into different Voronoi regions such that the $η$ within each Voronoi region share the same optimal PNC mapping $(α_{opt},β_{opt})$. We uncover the structure of the Voronoi regions that allows us to compute a minimum-distance metric that characterizes the SER of $w_N$ under optimal PNC mapping $(α_{opt},β_{opt})$. Overall, the contributions in (1) and (2) yield a toolset for a comprehensive understanding of complex linear PNC in $\mathbb{Z}[i]/q$. We believe investigation of linear PNC beyond $\mathbb{Z}[i]/q$ can follow the same approach.

cs.IT↗

arXiv2016

Optimal Rate-Diverse Wireless Network Coding

This paper proposes an encoding/decoding framework for achieving the optimal channel capacities of the two-user broadcast channel where each user (receiver) has the message targeted for the other user (receiver) as side information. Since the link qualities of the channels from the base station to the two users are different, their respective single-user non-broadcast channel capacities are also different. A goal is to simultaneously achieve/approach the single-user non-broadcast channel capacities of the two users with a single broadcast transmission by applying network coding. This is referred to as the \emph{rate-diverse wireless network coding} problem. For this problem, this paper presents a capacity-achieving framework based on linear- structured nested lattice codes. The significance of the proposed framework, besides its theoretical optimality, is that it suggests a general design principle for linear rate-diverse wireless network coding going beyond the use of lattice codes. We refer to this design principle as the \emph{principle of virtual single-user channels}. Guided by this design principle, we propose two implementations of our encoding/decoding framework using practical linear codes amenable to decoding with affordable complexities: the first implementation is based on Low Density Lattice Codes (LDLC) and the second implementation is based on Bit-interleaved Coded Modulation (BICM). These two implementations demonstrate the validity and performance advantage of our framework.

cs.IT↗

arXiv2014

The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations

In this work, we consider subordinated processes controlled by a family of subordinators which consist of a power function of time variable and a negative power function of $α-$stable random variable. The effect of parameters in the subordinators on the subordinated process is discussed. By suitable variable substitutions and Laplace transform technique, the corresponding fractional Fokker-Planck-type equations are derived. We also compute their mean square displacements in a free force field. By choosing suitable ranges of parameters, the resulting subordinated processes may be subdiffusive, normal diffusive or superdiffusive.

cond-mat.stat-mech↗

arXiv2014

On the Subtleties of q-PAM Linear Physical-Layer Network Coding

This paper investigates various subtleties of applying linear physical-layer network coding (PNC) with q-level pulse amplitude modulation (q-PAM) in two-way relay channels (TWRC). A critical issue is how the PNC system performs when the received powers from the two users at the relay are imbalanced. In particular, how would the PNC system perform under slight power imbalance that is inevitable in practice, even when power control is applied? To answer these questions, this paper presents a comprehensive analysis of q-PAM PNC. Our contributions are as follows: 1) We give a systematic way to obtain the analytical relationship between the minimum distance of the signal constellation induced by the superimposed signals of the two users (a key performance determining factor) and the channel-gain ratio of the two users, for all q. In particular, we show how the minimum distance changes in a piecewise linear fashion as the channel-gain ratio varies. 2) We show that the performance of q-PAM PNC is highly sensitive to imbalanced received powers from the two users at the relay, even when the power imbalance is slight (e.g., the residual power imbalance in a power-controlled system). This sensitivity problem is exacerbated as q increases, calling into question the robustness of high-order modulated PNC. 3) We propose an asynchronized PNC system in which the symbol arrival times of the two users at the relay are deliberately made to be asynchronous. We show that such asynchronized PNC, when operated with a belief propagation (BP) decoder, can remove the sensitivity problem, allowing a robust high-order modulated PNC system to be built.

cs.IT↗

arXiv2014

A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function $P(x,t)$ of finding the walker at position $x$ at time $t$ is completely determined by the Laplace transform of the probability density function $φ(t)$ of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

cond-mat.stat-mech↗

arXiv2013

Space-time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model

In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are discussed. The corresponding fractional diffusion equations are derived from the given asymptotic behaviors. Corresponding to the asymptotic behaviors of the joint probability density function in the Fourier-Laplace space, the asymptotic behaviors of the waiting time probability density and the conditional probability density for jump length are also discussed.

cond-mat.stat-mech↗

arXiv2012

On Designs of Full Diversity Space-Time Block Codes for Two-User MIMO Interference Channels

In this paper, a design criterion for space-time block codes (STBC) is proposed for two-user MIMO interference channels when a group zero-forcing (ZF) algorithm is applied at each receiver to eliminate the inter-user interference. Based on the design criterion, a design of STBC for two-user interference channels is proposed that can achieve full diversity for each user with the group ZF receiver. The code rate approaches one when the time delay in the encoding (or code block size) gets large. Performance results demonstrate that the full diversity can be guaranteed by our proposed STBC with the group ZF receiver.

cs.IT↗

arXiv2010

High-Rate and Full-Diversity Space-Time Block Codes with Low Complexity Partial Interference Cancellation Group Decoding

In this paper, we propose a systematic design of space-time block codes (STBC) which can achieve high rate and full diversity when the partial interference cancellation (PIC) group decoding is used at receivers. The proposed codes can be applied to any number of transmit antennas and admit a low decoding complexity while achieving full diversity. For M transmit antennas, in each codeword real and imaginary parts of PM complex information symbols are parsed into P diagonal layers and then encoded, respectively. With PIC group decoding, it is shown that the decoding complexity can be reduced to a joint decoding of M/2 real symbols. In particular, for 4 transmit antennas, the code has real symbol pairwise (i.e., single complex symbol) decoding that achieves full diversity and the code rate is 4/3. Simulation results demonstrate that the full diversity is offered by the newly proposed STBC with the PIC group decoding.

cs.IT↗

arXiv2010

Full Diversity Space-Time Block Codes with Low-Complexity Partial Interference Cancellation Group Decoding

Partial interference cancellation (PIC) group decoding proposed by Guo and Xia is an attractive low-complexity alternative to the optimal processing for multiple-input multiple-output (MIMO) wireless communications. It can well deal with the tradeoff among rate, diversity and complexity of space-time block codes (STBC). In this paper, a systematic design of full-diversity STBC with low-complexity PIC group decoding is proposed. The proposed code design is featured as a group-orthogonal STBC by replacing every element of an Alamouti code matrix with an elementary matrix composed of multiple diagonal layers of coded symbols. With the PIC group decoding and a particular grouping scheme, the proposed STBC can achieve full diversity, a rate of $(2M)/(M+2)$ and a low-complexity decoding for $M$ transmit antennas. Simulation results show that the proposed codes can achieve the full diversity with PIC group decoding while requiring half decoding complexity of the existing codes.

cs.IT↗