In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary rando...In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.展开更多
In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative par...In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive （or negative） central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.展开更多
In order to alleviate capacity constraints on the fronthaul and decrease the transmit latency, a hierarchical content caching paradigm is applied in the fog radio access networks(F-RANs). In particular, a specific clu...In order to alleviate capacity constraints on the fronthaul and decrease the transmit latency, a hierarchical content caching paradigm is applied in the fog radio access networks(F-RANs). In particular, a specific cluster of remote radio heads is formed through a common centralized cloud at the baseband unit pool, while the local content is directly delivered at fog access points with edge cache and distributed radio signal processing capability. Focusing on a downlink F-RAN, the explicit expressions of ergodic rate for the hierarchical paradigm is derived. Meanwhile, both the waiting delay and latency ratio for users requiring a single content are exploited. According to the evaluation results of ergodic rate on waiting delay, the transmit latency can be effectively reduced through improving the capacity of both fronthaul and radio access links. Moreover, to fully explore the potential of hierarchical content caching, the transmit latency for users requiring multiple content objects is optimized as well in three content transmission cases with different radio access links. The simulation results verify the accuracy of the analysis, further show the latency decreases significantly due to the hierarchical paradigm.展开更多
To ensure the security of a digital image, a new self-adapting encryption algorithm based on the spatiotemporal chaos and ergodic matrix is proposed in this paper. First, the plain-image is divided into different bloc...To ensure the security of a digital image, a new self-adapting encryption algorithm based on the spatiotemporal chaos and ergodic matrix is proposed in this paper. First, the plain-image is divided into different blocks of the same size, and each block is sorted in ascending order to obtain the corresponding standard ergodic matrix. Then each block is encrypted by the spatiotemporal chaotic system and shuffled according to the standard ergodic matrix. Finally, all modules are rearranged to acquire the final encrypted image. In particular, the plain-image information is used in the initial conditions of the spatiotemporal chaos and the ergodic matrices, so different plain-images will be encrypted to obtain different cipherimages. Theoretical analysis and simulation results indicate that the performance and security of the proposed encryption scheme can encrypt the image effectively and resist various typical attacks.展开更多
This paper deals with the coverage analysis problem of elliptical orbits. An algorithm based on ergodic theory, for long-term coverage of elliptical orbits, is proposed. The differential form of the invariant measure ...This paper deals with the coverage analysis problem of elliptical orbits. An algorithm based on ergodic theory, for long-term coverage of elliptical orbits, is proposed. The differential form of the invariant measure is constructed via the perturbation on mean orbital elements resulted from the J2 term of non-spherical shape of the earth. A rigorous proof for this is then given. Different from the case of circular orbits, here the flow and its space of the dynamical system are defined on a physical space, and the real-value function is defined as the characteristic function on station mask. Therefore, the long-term coverage is reduced to a double integral via Birkhoff-Khinchin theorem. The numerical implementation indicates that the ergodic algorithm developed is available for a wide range of eccentricities.展开更多
By reusing the spectrum of a cellular network, device-to-device(D2D) communications is known to greatly improve the spectral efficiency bypassing the base station(BS) of the cellular network. Antenna selection is the ...By reusing the spectrum of a cellular network, device-to-device(D2D) communications is known to greatly improve the spectral efficiency bypassing the base station(BS) of the cellular network. Antenna selection is the most cost efficient scheme for interference management, which is crucial to D2D systems. This paper investigates the achievable rate performance of the D2D communication underlaying the cellular network where a multiple-antenna base station with antenna selection scheme is deployed. We derive an exact closed-form expression of the ergodic achievable rate. Also, using Jensen's inequality, two pairs of upper and lower bounds of the rate are derived and we validate the tightness of the two sets of bounds. Based on the bounds obtained, we analyze the ergodic achievable rate in noise-limited scenario, interference-limited high SNR scenario and larger-scale antenna systems. Our analysis shows that the presence of D2D users could be counter-productive if the SNR at cellular UE is high. Further analysis shows that the relationship between the ergodic rate and the number of antennas it positive, but keeps decreasing as the antenna number increasing. These show the inefficiency of antenna selection in D2D interference management.展开更多
In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to...In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.展开更多
The ergodic information rate for Orthogonal Frequency-Division Multiplexing / Orthogonal Frequency-Division Multiple Access with amplify-and-forward （AF） relaying systems in the presence of frequency offsets is eval...The ergodic information rate for Orthogonal Frequency-Division Multiplexing / Orthogonal Frequency-Division Multiple Access with amplify-and-forward （AF） relaying systems in the presence of frequency offsets is evaluated. Unlike previous work, per-subcarrier adaptive power allocation is performed on each relay to optimize the system ergodic information rate. For a given frequency offset and total number of relays M, the AF ergodic information rate is proven to be a monotonically increasing function of α （the ratio of the power allocated to the source node and the total transmit power）, implying that the maximum ergodic information rate can be obtained at α=1 （i.e., there is no cooperative relay）. Furthermore, the proof of ＂cooperative relays cannot improve the AF ergodic information rate in a quasi-static wireless channel＂ is also provided in this letter.展开更多
In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this sche...In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this scheme to encrypt plaintext and obtain ciphertext. In this algorithm, the plaintext information in the key is used, so different plaintexts or different total numbers of plaintext letters will encrypt different ciphertexts. Simulation results show that the performance and the security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.展开更多
In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and L^p convergence as well as maximal inequalities, which are established both in ergodic theory and martingale sett...In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and L^p convergence as well as maximal inequalities, which are established both in ergodic theory and martingale setting, also hold well for these new sequences of random variables. Moreover, the corresponding theorems in the former two areas turn out to be degenerate cases of the martingale ergodic theorems proved here.展开更多
In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netiz...In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.展开更多
Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where ...Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.展开更多
Recently, Mao, Zhang, Wu et al. constructed two key exchange(KE) protocols based on tensor ergodic problem(TEP). Although they conjectured that these constructions can potentially resist quantum computing attack, they...Recently, Mao, Zhang, Wu et al. constructed two key exchange(KE) protocols based on tensor ergodic problem(TEP). Although they conjectured that these constructions can potentially resist quantum computing attack, they did not provide a rigorous security proof for their KE protocols. In this paper, applying the properties of ergodic matrix, we first present a polynomial time algorithm to solve the TEP problem using O(n^6) arithmetic operations in the finite field, where n is the security parameter. Then, applying this polynomial time algorithm, we generate a common shared key for two TEP-based KE constructions, respectively. In addition, we also provide a polynomial time algorithm with O(n^6) arithmetic operations that directly recovers the plaintext from a ciphertext for the KE-based encryption scheme. Thus, the TEP-based KE protocols and their corresponding encryption schemes are insecure.展开更多
The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[1...The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[10].In this paper,we shall give the su？cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.展开更多
Bandwidth,cutwidth,cyclic bandwidth,bandwidth sum and cyclic bandwidth sum are well-known indices about optimal labeling of graphs applied in VLSI design,network communications,and other areas involving the graph layo...Bandwidth,cutwidth,cyclic bandwidth,bandwidth sum and cyclic bandwidth sum are well-known indices about optimal labeling of graphs applied in VLSI design,network communications,and other areas involving the graph layout.To design the graphs with the given indices,we need to study the ergodicity.Let F be a set of graphs under consideration andφan integer-valued function defined on F,namely,φis an index,such as bandwidth and cutwidth.If there exists a graph G∈F such thatφ(G)=x for any integer x in the interval[a,b],where a and b are the minimum and maximum ofφon F,respectively,thenφis said to have ergodicity on F.Let Gnbe the set of simple connected graphs with order n and Tnthe set of trees with order n.In this paper,we investigate the ergodicity of bandwidth,cutwidth,cyclic bandwidth,the bandwidth sum and cyclic bandwidth sum on Tn and Gn.展开更多
Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning mas...Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning massive reflecting elements.This paper considers a distributed IRS aided decode-and-forward(DF)relaying system over Nakagami-m fading channels.Based on a tight approximation for the distribution of the received signalto-noise ratio(SNR),we first derive exact closed-form expressions of the outage probability,ergodic capacity,and energy efficiency for the considered system.Moreover,we propose the optimal IRS configuration considering the energy efficiency and pilot overhead.Finally,we compare the performance between the distributed IRS-aided DF relaying and multi-IRS-only systems,and verify the analytical results by using monte carlo simulations.展开更多
The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant qua...The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and eneryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security,security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.展开更多
In this paper,an energy harvesting enabled cooperative non-orthogonal multiple access(NOMA)system for a multi-cell network is investigated.Particularly,during the direct transmission phase,base stations send their sup...In this paper,an energy harvesting enabled cooperative non-orthogonal multiple access(NOMA)system for a multi-cell network is investigated.Particularly,during the direct transmission phase,base stations send their superposed messages to the near users and far users simultaneously according to a NOMA principle,while the near users act as energy harvesting enabled relays employing a power splitting protocol.During the cooperative phase,the near users transmit their decoded messages to the corresponding far users using harvested energy.Using tools from stochastic geometry,we firstly calculate the signal to interference ratios of the users in each NOMA group including one near user and one far user.Then,the closed-form expressions of the coverage probability,ergodic rate,and energy efficiency are derived respectively.Numerical results validate the derived expressions and show that the energy harvesting enabled cooperative NOMA system in a multi-cell network can improve the coverage probability,ergodic rate,and energy efficiency compared to its counterpart OMA system.展开更多
基金supported by the Shenzhen sustainable development project:KCXFZ 20201221173013036 and the National Natural Science Foundation of China(91746107).
文摘In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.
基金Supported by the National Natural Science Foundation of China(11071053)Natural Science Foundation of Hebei Province(A2014207010)+2 种基金Key Project of Science and Research of Hebei Educational Department(ZD2016024)Key Project of Science and Research of Hebei University of Economics and Business(2016KYZ07)the third author is supported by Science and Technology Foundation of Agricultural University of Hebei(LG201612)
基金supported by National Natural Science Foundation of China(11001284)Natural Science Foundation Project of CQ CSTC(cstcjjA00003)Fundamental Research Funds for the Central Universities(CQDXWL2012008)
文摘In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive （or negative） central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.
基金supported in part by the National Natural Science Foundation of China (Grant No.61361166005)the State Major Science and Technology Special Projects (Grant No.2016ZX03001020006)the National Program for Support of Top-notch Young Professionals
文摘In order to alleviate capacity constraints on the fronthaul and decrease the transmit latency, a hierarchical content caching paradigm is applied in the fog radio access networks(F-RANs). In particular, a specific cluster of remote radio heads is formed through a common centralized cloud at the baseband unit pool, while the local content is directly delivered at fog access points with edge cache and distributed radio signal processing capability. Focusing on a downlink F-RAN, the explicit expressions of ergodic rate for the hierarchical paradigm is derived. Meanwhile, both the waiting delay and latency ratio for users requiring a single content are exploited. According to the evaluation results of ergodic rate on waiting delay, the transmit latency can be effectively reduced through improving the capacity of both fronthaul and radio access links. Moreover, to fully explore the potential of hierarchical content caching, the transmit latency for users requiring multiple content objects is optimized as well in three content transmission cases with different radio access links. The simulation results verify the accuracy of the analysis, further show the latency decreases significantly due to the hierarchical paradigm.
基金supported by the National Natural Science Foundation of China(Grant Nos.U0735004 and 60972133)the Natural Science Foundation of Guangdong Province,China(Grant No.05006593)+2 种基金the Project Team for Natural Science Foundation of Guangdong Province,China(Grant No.9351064101000003)Energy Technology Key Laboratory Project of Guangdong Province,China(Grant No.2008A060301002)the Fundamental Research Funds for the Central Universities,China(Grant No.X2dXD2116370)
文摘To ensure the security of a digital image, a new self-adapting encryption algorithm based on the spatiotemporal chaos and ergodic matrix is proposed in this paper. First, the plain-image is divided into different blocks of the same size, and each block is sorted in ascending order to obtain the corresponding standard ergodic matrix. Then each block is encrypted by the spatiotemporal chaotic system and shuffled according to the standard ergodic matrix. Finally, all modules are rearranged to acquire the final encrypted image. In particular, the plain-image information is used in the initial conditions of the spatiotemporal chaos and the ergodic matrices, so different plain-images will be encrypted to obtain different cipherimages. Theoretical analysis and simulation results indicate that the performance and security of the proposed encryption scheme can encrypt the image effectively and resist various typical attacks.
基金Project supported by the Innovation Foundation of BUAA (Beijing University of Aeronautics and Astronautics) for PhD Graduatesthe National Natural Science Foundation of China (Grant No 60535010)
文摘This paper deals with the coverage analysis problem of elliptical orbits. An algorithm based on ergodic theory, for long-term coverage of elliptical orbits, is proposed. The differential form of the invariant measure is constructed via the perturbation on mean orbital elements resulted from the J2 term of non-spherical shape of the earth. A rigorous proof for this is then given. Different from the case of circular orbits, here the flow and its space of the dynamical system are defined on a physical space, and the real-value function is defined as the characteristic function on station mask. Therefore, the long-term coverage is reduced to a double integral via Birkhoff-Khinchin theorem. The numerical implementation indicates that the ergodic algorithm developed is available for a wide range of eccentricities.
基金supported by National Natural Science Foundation of China (61671080)
文摘By reusing the spectrum of a cellular network, device-to-device(D2D) communications is known to greatly improve the spectral efficiency bypassing the base station(BS) of the cellular network. Antenna selection is the most cost efficient scheme for interference management, which is crucial to D2D systems. This paper investigates the achievable rate performance of the D2D communication underlaying the cellular network where a multiple-antenna base station with antenna selection scheme is deployed. We derive an exact closed-form expression of the ergodic achievable rate. Also, using Jensen's inequality, two pairs of upper and lower bounds of the rate are derived and we validate the tightness of the two sets of bounds. Based on the bounds obtained, we analyze the ergodic achievable rate in noise-limited scenario, interference-limited high SNR scenario and larger-scale antenna systems. Our analysis shows that the presence of D2D users could be counter-productive if the SNR at cellular UE is high. Further analysis shows that the relationship between the ergodic rate and the number of antennas it positive, but keeps decreasing as the antenna number increasing. These show the inefficiency of antenna selection in D2D interference management.
基金supported by the National Science Foundation of China(1067121290820302)the National Science Foundation of Hunan Province
文摘In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.
基金the 863 project No.2014AA01A701,the National Natural Science Foundation of China，Program for New Century Excellent Talents in University，the open research fund of National Mobile Communications Research Laboratory Southeast University，the Research Foundation of China Mobile,and the Foundation of Beijing Engineering and Technology Center for Convergence Networks and Ubiquitous Services
文摘The ergodic information rate for Orthogonal Frequency-Division Multiplexing / Orthogonal Frequency-Division Multiple Access with amplify-and-forward （AF） relaying systems in the presence of frequency offsets is evaluated. Unlike previous work, per-subcarrier adaptive power allocation is performed on each relay to optimize the system ergodic information rate. For a given frequency offset and total number of relays M, the AF ergodic information rate is proven to be a monotonically increasing function of α （the ratio of the power allocated to the source node and the total transmit power）, implying that the maximum ergodic information rate can be obtained at α=1 （i.e., there is no cooperative relay）. Furthermore, the proof of ＂cooperative relays cannot improve the AF ergodic information rate in a quasi-static wireless channel＂ is also provided in this letter.
基金supported by the National Natural Science Foundation of China (Grant Nos.61173183,60973152,and 60573172)the Superior University Doctor Subject Special Scientific Research Foundation of China (Grant No.20070141014)the Natural Science Foundation of Liaoning Province,China (Grant No.20082165)
文摘In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this scheme to encrypt plaintext and obtain ciphertext. In this algorithm, the plaintext information in the key is used, so different plaintexts or different total numbers of plaintext letters will encrypt different ciphertexts. Simulation results show that the performance and the security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.
文摘In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and L^p convergence as well as maximal inequalities, which are established both in ergodic theory and martingale setting, also hold well for these new sequences of random variables. Moreover, the corresponding theorems in the former two areas turn out to be degenerate cases of the martingale ergodic theorems proved here.
基金supported by the Funding for Outstanding Doctoral Dissertation in NUAA(Grant No.BCXJ18-09)the National Natural Science Foundation of China(Grant No.72071106)Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX180234)。
文摘In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.
文摘Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.
基金supported by the National Natural Science Foundation of China(No.61672270,61602216,61702236)the Qing Lan Project for Young Researchers of Jiangsu Province of China(No.KYQ14004)+1 种基金the Open Fund of State Key Laboratory of Information Security,Institute of Information Engineering,Chinese Academy of Sciences(No.2015-MSB-10)Jiangsu Overseas Research&Training Program for University Prominent Young&Middle-aged Teachers and Presidents,Changzhou Sci&Tech Program,(Grant No.CJ20179027)
文摘Recently, Mao, Zhang, Wu et al. constructed two key exchange(KE) protocols based on tensor ergodic problem(TEP). Although they conjectured that these constructions can potentially resist quantum computing attack, they did not provide a rigorous security proof for their KE protocols. In this paper, applying the properties of ergodic matrix, we first present a polynomial time algorithm to solve the TEP problem using O(n^6) arithmetic operations in the finite field, where n is the security parameter. Then, applying this polynomial time algorithm, we generate a common shared key for two TEP-based KE constructions, respectively. In addition, we also provide a polynomial time algorithm with O(n^6) arithmetic operations that directly recovers the plaintext from a ciphertext for the KE-based encryption scheme. Thus, the TEP-based KE protocols and their corresponding encryption schemes are insecure.
基金Supported by the Chinese Universities Scientific Fund(BUPT2009RC0707,BUPT2011RC0703)
文摘The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[10].In this paper,we shall give the su？cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.
基金Supported by Science and Technology Program of Guangzhou(Grant No.202002030183)Natural Science Foundation of Guangdong(Grant No.2021A1515012045)+1 种基金National Natural Science Foundation of China(Grant No.12161073)Natural Science Foundation of Qinghai(Grant No.2020-ZJ-924)。
文摘Bandwidth,cutwidth,cyclic bandwidth,bandwidth sum and cyclic bandwidth sum are well-known indices about optimal labeling of graphs applied in VLSI design,network communications,and other areas involving the graph layout.To design the graphs with the given indices,we need to study the ergodicity.Let F be a set of graphs under consideration andφan integer-valued function defined on F,namely,φis an index,such as bandwidth and cutwidth.If there exists a graph G∈F such thatφ(G)=x for any integer x in the interval[a,b],where a and b are the minimum and maximum ofφon F,respectively,thenφis said to have ergodicity on F.Let Gnbe the set of simple connected graphs with order n and Tnthe set of trees with order n.In this paper,we investigate the ergodicity of bandwidth,cutwidth,cyclic bandwidth,the bandwidth sum and cyclic bandwidth sum on Tn and Gn.
基金supported in part by National Natural Science Foundation of China under Grant 62371262 and 61971467in part by the Key Research and Development Program of Jiangsu Province of China under Grant BE2021013-1+1 种基金in part by the Qinlan Project of Jiangsu Provincein part by the Scientific Research Program of Nantong under Grant JC22022026
文摘Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning massive reflecting elements.This paper considers a distributed IRS aided decode-and-forward(DF)relaying system over Nakagami-m fading channels.Based on a tight approximation for the distribution of the received signalto-noise ratio(SNR),we first derive exact closed-form expressions of the outage probability,ergodic capacity,and energy efficiency for the considered system.Moreover,we propose the optimal IRS configuration considering the energy efficiency and pilot overhead.Finally,we compare the performance between the distributed IRS-aided DF relaying and multi-IRS-only systems,and verify the analytical results by using monte carlo simulations.
基金the National Natural Science Foundation of China，the State Key Program of National Natural Science of China，the Major Research Plan of the National Natural Science Foundation of China，Major State Basic Research Development Program of China (973 Program)，the Hubei Natural Science Foundation of China
文摘The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and eneryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security,security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.
基金supported in part by National Natural Science Foundation of China (61771358)Intergovernmental International Cooperation on Science and Technology Innovation (2016YFE0123200)+2 种基金China Postdoctoral Science Foundation (2017M613074)Fundamental Research Funds for the Central Universities (JB170102)the 111 Project (B08038)
文摘In this paper,an energy harvesting enabled cooperative non-orthogonal multiple access(NOMA)system for a multi-cell network is investigated.Particularly,during the direct transmission phase,base stations send their superposed messages to the near users and far users simultaneously according to a NOMA principle,while the near users act as energy harvesting enabled relays employing a power splitting protocol.During the cooperative phase,the near users transmit their decoded messages to the corresponding far users using harvested energy.Using tools from stochastic geometry,we firstly calculate the signal to interference ratios of the users in each NOMA group including one near user and one far user.Then,the closed-form expressions of the coverage probability,ergodic rate,and energy efficiency are derived respectively.Numerical results validate the derived expressions and show that the energy harvesting enabled cooperative NOMA system in a multi-cell network can improve the coverage probability,ergodic rate,and energy efficiency compared to its counterpart OMA system.
