arXiv subjects

Fan Wei

Publications and source records attributed to Fan Wei.

At least 55 records · Page 3Linked to original sources

arXiv2020

Low Complexity Iterative Receiver Design for Sparse Code Multiple Access

Sparse code multiple access (SCMA) is one of the most promising methods among all the non-orthogonal multiple access techniques in the future 5G communication. Compared with some other non-orthogonal multiple access techniques such as low density signature (LDS), SCMA can achieve better performance due to the shaping gain of the SCMA codewords. However, despite of the sparsity of the codewords, the decoding complexity of the current message passing algorithm (MPA) utilized by SCMA is still prohibitively high. In this paper, by exploring the lattice structure of SCMA codewords, we propose a low complexity decoding algorithm based on list sphere decoding (LSD). The LSD avoids the exhaustive search for all possible hypotheses and only considers signal within a hypersphere. As LSD can be viewed a depth-first tree search algorithm, we further propose several methods to prune the redundancy visited nodes in order to reduce the size of the search tree. Simulation results show that the proposed algorithm can reduce the decoding complexity substantially while the performance loss compared with the existing algorithm is negligible.

eess.SP↗

arXiv2019

Random Pilot and Data Access for Massive MIMO Spatially Correlated Rayleigh Fading Channels

Random access is necessary in crowded scenarios due to the limitation of pilot sequences and the intermittent pattern of device activity. Nowadays, most of the related works are based on independent and identically distributed (i.i.d.) channels. However, massive multiple-input multiple-output (MIMO) channels are not always i.i.d. in realistic outdoor wireless propagation environments. In this paper, a device grouping and pilot set allocation algorithm is proposed for the uplink massive MIMO systems over spatially correlated Rayleigh fading channels. Firstly, devices are divided into multiple groups, and the channel covariance matrixes of devices within the same group are approximately orthogonal. In each group, a dedicated pilot set is assigned. Then active devices perform random pilot and data access process. The mean square error of channel estimation (MSE-CE) and the spectral efficiency of this scheme are derived, and the MSE-CE can be minimized when collision devices have non-overlapping angle of arrival (AoA) intervals. Simulation results indicate that the MSE-CE and spectral efficiency of this protocol are improved compared with the traditional scheme. The MSE-CE of the proposed scheme is close to the theoretical lower bound over a wide signal-to-noise ratio (SNR) region especially for long pilot sequence. Furthermore, the MSE-CE performance gains are significant in high SNR and strongly correlated scenarios.

eess.SP↗

arXiv2019

On the Fundamental Limits of MIMO Massive Access Communication

The multiple access channel (MAC) with many-user is a general model for massive machine type communications. In this paradigm, the number of users may be comparable or even larger than the coding blocklength $n$. In contrast, classical MAC often assumes fixed and small number of the users. In this paper, we consider the massive access channel with multiple antennas system, where the base station (BS) with multiple receiving antennas serves the users in a single cell. The magnitude of users is assumed to grow unbounded with $n$. We investigate the achievable region of MIMO massive access channel, where among the total users, an unknown subset referred to active users may transmit data periodically. The asymptotic active user identification cost is also quantified. With the theoretical analysis, it was shown that given finite number of the receiving antennas, the individual rate for each user can be formulated as the sum rate multiplied by some specific factors, which correspond to the allocation of sum capacity. The successive decoding does not apply due to the interferences from growing unbounded users. Theoretical analysis shows that successive decoding works only when the number of receiving antennas goes to infinity with the increasing codelength.

cs.IT↗

arXiv2019

On the Fundamental Limits of MIMO Massive Multiple Access Channels

In this paper, we study the multiple-antenna wireless communication networks, where a large number of devices simultaneously communicate with an access point. The capacity region of multiple-input multiple-output massive multiple access channels (MIMO mMAC) is investigated. While joint typicality decoding is utilized to establish the achievability of capacity region for conventional MAC with fixed number of users, the technique is not directly applicable for MIMO mMAC. Instead, an information-theoretic approach based on Gallager's error exponent analysis is exploited to characterize the \textcolor[rgb]{0,0,0}{finite dimension region} of MIMO mMAC. Theoretical results reveal that the finite dimension region of MIMO mMAC is dominated by sum rate constraint only, and the individual user rate is determined by a specific factor that corresponds to the allocation of sum rate. The rate in conventional MAC is not achievable with massive multiple access, which is due to the fact that successive interference cancellation cannot guarantee an arbitrary small error decoding probability for MIMO mMAC. The results further imply that, asymptotically, the individual user rate is independent of the number of transmit antennas, and channel hardening makes the individual user rate close to that when only statistic knowledge of channel is available at receiver. The finite dimension region of MIMO mMAC is a generalization of the symmetric rate in Chen \emph{et al.} (2017).

cs.IT↗

arXiv2018

MIMO-OFDM Scheme design for Medium Voltage Underground Cables based Power Line Communication

Power line communication (PLC) provides intelligent electrical functions such as power quality measurement, fault surveys, and remote control of electrical network. However, most of research works have been done in low voltage (LV) scenario due to the fast development of in-home PLC. The aim of this paper is to design a MIMO-OFDM based transmission link under medium voltage (MV) underground power line channel and evaluate the performance. The MIMO channel is modeled as a modified multipath model in the presence of impulsive noise and background noise. Unlike most literatures on MIMO power line transmission, we adopt spatial multiplexing instead of diversity to increase the transmission rate in this paper. The turbo coding method originally designed for LV power line communication is used in the proposed transmission system. By comparing the BER performance of MIMO-OFDM system with and without the turbo coding, we evaluate its applicability in MV power line communication. The effect of frequency band varying on the PLC system's performance is also investigated.

cs.IT↗

arXiv2018

On the number of cliques in graphs with a forbidden subdivision or immersion

How many cliques can a graph on $n$ vertices have with a forbidden substructure? Extremal problems of this sort have been studied for a long time. This paper studies the maximum possible number of cliques in a graph on $n$ vertices with a forbidden clique subdivision or immersion. We prove for $t$ sufficiently large that every graph on $n \geq t$ vertices with no $K_t$-immersion has at most $2^{t+\log^2 t}n$ cliques, which is sharp apart from the $2^{O(\log^2 t)}$ factor. We also prove that the maximum number of cliques in an $n$-vertex graph with no $K_t$-subdivision is at most $2^{1.817t}n$. This improves on the best known exponential constant by Lee and Oum. We conjecture that the optimal bound is $3^{2t/3 +o(t)}n$, as we proved for minors in place of subdivision in earlier work.

math.CO↗

arXiv2018

Finding Cliques in Social Networks: A New Distribution-Free Model

We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be adjacent. Our most basic definition is that of a "$c$-closed" graph, where for every pair of vertices $u,v$ with at least $c$ common neighbors, $u$ and $v$ are adjacent. We study the classic problem of enumerating all maximal cliques, an important task in social network analysis. We prove that this problem is fixed-parameter tractable with respect to $c$ on $c$-closed graphs. Our results carry over to "weakly $c$-closed graphs", which only require a vertex deletion ordering that avoids pairs of non-adjacent vertices with $c$ common neighbors. Numerical experiments show that well-studied social networks tend to be weakly $c$-closed for modest values of $c$.

math.CO↗

arXiv2018

Fast property testing and metrics for permutations

The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $ε$-far from satisfying the property. There are now several general results in this area which show that natural properties of combinatorial objects can be tested with "constant" query complexity, depending only on $ε$ and the property, and not on the size of the object being tested. The upper bound on the query complexity coming from the proof techniques are often enormous and impractical. It remains a major open problem if better bounds hold. Maybe surprisingly, for testing with respect to the rectangular distance, we prove there is a universal (not depending on the property), polynomial in $1/ε$ query complexity bound for two-sided testing hereditary properties of sufficiently large permutations. We further give a nearly linear bound with respect to a closely related metric which also depends on the smallest forbidden subpermutation for the property. Finally, we show that several different permutation metrics of interest are related to the rectangular distance, yielding similar results for testing with respect to these metrics.

math.CO↗

arXiv2017

Message-Passing Receiver Design for Joint Channel Estimation and Data Decoding in Uplink Grant-Free SCMA Systems

The conventional grant-based network relies on the handshaking between base station and active users to achieve dynamic multi-user scheduling, which may cost large signaling overheads as well as system latency. To address those problems, the grant-free receiver design is considered in this paper based on sparse code multiple access (SCMA), one of the promising air interface technologies for 5G wireless networks. With the presence of unknown multipath fading, the proposed receiver blindly performs joint channel estimation and data decoding without knowing the user activity in the network. Based on the framework of belief propagation (BP), we formulate a messagepassing receiver for uplink SCMA that performs joint estimation iteratively. However, the direct application of BP for the multivariable detection problem is complex. Motivated by the idea of approximate inference, we use expectation propagation to project the intractable distributions into Gaussian families such that a linear complexity decoder is obtained.Simulation results show that the proposed receiver can detect active users in the network with a high accuracy and can achieve an improved bit-error-rate performance compared with existing methods.

eess.SP↗

arXiv2017

Local max-cut in smoothed polynomial time

In 1988, Johnson, Papadimitriou and Yannakakis wrote that "Practically all the empirical evidence would lead us to conclude that finding locally optimal solutions is much easier than solving NP-hard problems". Since then the empirical evidence has continued to amass, but formal proofs of this phenomenon have remained elusive. A canonical (and indeed complete) example is the local max-cut problem, for which no polynomial time method is known. In a breakthrough paper, Etscheid and Röglin proved that the smoothed complexity of local max-cut is quasi-polynomial, i.e., if arbitrary bounded weights are randomly perturbed, a local maximum can be found in $n^{O(\log n)}$ steps. In this paper we prove smoothed polynomial complexity for local max-cut, thus confirming that finding local optima for max-cut is much easier than solving it.

cs.DS↗

arXiv2017

Self-Paced Multi-Task Learning

In this paper, we propose a novel multi-task learning (MTL) framework, called Self-Paced Multi-Task Learning (SPMTL). Different from previous works treating all tasks and instances equally when training, SPMTL attempts to jointly learn the tasks by taking into consideration the complexities of both tasks and instances. This is inspired by the cognitive process of human brain that often learns from the easy to the hard. We construct a compact SPMTL formulation by proposing a new task-oriented regularizer that can jointly prioritize the tasks and the instances. Thus it can be interpreted as a self-paced learner for MTL. A simple yet effective algorithm is designed for optimizing the proposed objective function. An error bound for a simplified formulation is also analyzed theoretically. Experimental results on toy and real-world datasets demonstrate the effectiveness of the proposed approach, compared to the state-of-the-art methods.

cs.LG↗

arXiv2016

A Self-Paced Regularization Framework for Multi-Label Learning

In this paper, we propose a novel multi-label learning framework, called Multi-Label Self-Paced Learning (MLSPL), in an attempt to incorporate the self-paced learning strategy into multi-label learning regime. In light of the benefits of adopting the easy-to-hard strategy proposed by self-paced learning, the devised MLSPL aims to learn multiple labels jointly by gradually including label learning tasks and instances into model training from the easy to the hard. We first introduce a self-paced function as a regularizer in the multi-label learning formulation, so as to simultaneously rank priorities of the label learning tasks and the instances in each learning iteration. Considering that different multi-label learning scenarios often need different self-paced schemes during optimization, we thus propose a general way to find the desired self-paced functions. Experimental results on three benchmark datasets suggest the state-of-the-art performance of our approach.

cs.LG↗

arXiv2016

On the number of cliques in graphs with a forbidden minor

Reed and Wood and independently Norine, Seymour, Thomas, and Wollan proved that for each positive integer $t$ there is a constant $c(t)$ such that every graph on $n$ vertices with no $K_t$-minor has at most $c(t)n$ cliques. Wood asked in 2007 if we can take $c(t) = c^t$ for some absolute constant $c$. This question was recently answered affirmatively by Lee and Oum. In this paper, we determine the exponential constant. We prove that every graph on $n$ vertices with no $K_t$-minor has at most $3^{2t/3+o(t)}n$ cliques. This bound is tight for $n \geq 4t/3$. More generally, let $H$ be a connected graph on $t$ vertices, and $x$ denote the size (i.e., the number edges) of the largest matching in the complement of $H$. We prove that every graph on $n$ vertices with no $H$-minor has at most $\max(3^{2t/3-x/3+o(t)}n,2^{t+o(t)}n)$ cliques, and this bound is tight for $n \geq \max (4t/3-2x/3,t)$ by a simple construction. Even more generally, we determine explicitly the exponential constant for the maximum number of cliques an $n$-vertex graph can have in a minor-closed family of graphs which is closed under disjoint union.

math.CO↗

arXiv2015

Quantum Phase diagram and time-of-flight absorption pictures of ultracold Bose system in a square optical superlattice

In this letter, by the use of the generalized effective potential theory, with the help of process-chain approach under the framework of Kato formulation of perturbation expansion, we calculate out the quantum phase diagram up to 8-th order for an ultracold Bose system in a square optical superlattice. Base on these perturbative data, with the help of the linear fit extrapolation technique, more accurate results are gotten, which are in excellent agreement with recent Monte-Carlo numerical results. Moreover, by employing the generalized re-summed Green's function method and cumulant expansion, the momentum distribution function of the system is also calculated analytically and the time-of-flight absorption pictures of the system are plotted.

cond-mat.quant-gas↗

arXiv2015

Dynamic Structure Embedded Online Multiple-Output Regression for Stream Data

Online multiple-output regression is an important machine learning technique for modeling, predicting, and compressing multi-dimensional correlated data streams. In this paper, we propose a novel online multiple-output regression method, called MORES, for stream data. MORES can \emph{dynamically} learn the structure of the coefficients change in each update step to facilitate the model's continuous refinement. We observe that limited expressive ability of the regression model, especially in the preliminary stage of online update, often leads to the variables in the residual errors being dependent. In light of this point, MORES intends to \emph{dynamically} learn and leverage the structure of the residual errors to improve the prediction accuracy. Moreover, we define three statistical variables to \emph{exactly} represent all the seen samples for \emph{incrementally} calculating prediction loss in each online update round, which can avoid loading all the training data into memory for updating model, and also effectively prevent drastic fluctuation of the model in the presence of noise. Furthermore, we introduce a forgetting factor to set different weights on samples so as to track the data streams' evolving characteristics quickly from the latest samples. Experiments on one synthetic dataset and three real-world datasets validate the effectiveness of the proposed method. In addition, the update speed of MORES is at least 2000 samples processed per second on the three real-world datasets, more than 15 times faster than the state-of-the-art online learning algorithm.

cs.LG↗

arXiv2013

Involutions on standard Young tableaux and divisors on metric graphs

We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the $v_0$-reduced divisors (representatives of the equivalence classes) associated to given tableaux, and use this formula to prove (i) evacuation of tableaux corresponds (under the bijection) to reflecting the metric graph, and (ii) conjugation of the tableaux corresponds to taking the Riemann-Roch dual of the divisor.

math.CO↗

arXiv2011

Dvoretzky--Kiefer--Wolfowitz Inequalities for the Two-sample Case

The Dvoretzky--Kiefer--Wolfowitz (DKW) inequality says that if $F_n$ is an empirical distribution function for variables i.i.d.\ with a distribution function $F$, and $K_n$ is the Kolmogorov statistic $\sqrt{n}\sup_x|(F_n-F)(x)|$, then there is a finite constant $C$ such that for any $M>0$, $\Pr(K_n>M) \leq C\exp(-2M^2).$ Massart proved that one can take C=2 (DKWM inequality) which is sharp for $F$ continuous. We consider the analogous Kolmogorov--Smirnov statistic $KS_{m,n}$ for the two-sample case and show that for $m=n$, the DKW inequality holds with C=2 if and only if $n\geq 458$. For $n_0\leq n<458$ it holds for some $C>2$ depending on $n_0$. For $m\neq n$, the DKWM inequality fails for the three pairs $(m,n)$ with $1\leq m < n\leq 3$. We found by computer search that for $n\geq 4$, the DKWM inequality always holds for $1\leq m< n\leq 200$, and further that it holds for $n=2m$ with $101\leq m\leq 300$. We conjecture that the DKWM inequality holds for pairs $m\leq n$ with the $457+3 =460$ exceptions mentioned.

math.ST↗

arXiv2010

The Weak Bruhat Order and Separable Permutations

In this paper we consider the rank generating function of a separable permutation $π$ in the weak Bruhat order on the two intervals $[\text{id}, π]$ and $[π, w_0]$, where $w_0 = n,(n-1),..., 1$. We show a surprising result that the product of these two generating functions is the generating function for the symmetric group with the weak order. We then obtain explicit formulas for the rank generating functions on $[\text{id}, π]$ and $[π, w_0]$, which leads to the rank-symmetry and unimodality of the two graded posets.

math.CO↗