This article proposes and demonstrates a retrodirective array(RDA)for two-way wireless communication with automatic beam tracking.The proposed RDA is enabled by specifically designed chips made using a domestic comple...This article proposes and demonstrates a retrodirective array(RDA)for two-way wireless communication with automatic beam tracking.The proposed RDA is enabled by specifically designed chips made using a domestic complementary metal-oxide semiconductor(CMOS)process.The highly integrated CMOS chip includes a receiving(Rx)chain,a transmitting(Tx)chain,and a unique tracking phaselocked loop(PLL)for the crucial conjugated phase recovery in the RDA.This article also proposes a method to reduce the beam pointing error(BPE)in a conventional RDA.To validate the above ideas simply yet without loss of generality,a 2.4 GHz RDA is demonstrated through two-way communication links between the Rx and Tx chains,and an on-chip quadrature coupler is designed to achieve a nonretrodirective signal suppression of 23 dBc.The experimental results demonstrate that the proposed RDA,which incorporates domestically manufactured low-cost 0.18 lm CMOS chips,is capable of automatically tracking beams covering±40with a reduced BPE.Each CMOS chip in the RDA has a compact size of 4.62 mm^(2) and a low power consumption of 0.15 W.To the best of the authors’knowledge,this is the first research to demonstrate an RDA with a fully customized CMOS chip for wireless communication with automatic beam tracking。展开更多
The data post-processing scheme based on two-way classical communication(TWCC)can improve the tolerable bit error rate and extend the maximal transmission distance when used in a quantum key distribution(QKD)system.In...The data post-processing scheme based on two-way classical communication(TWCC)can improve the tolerable bit error rate and extend the maximal transmission distance when used in a quantum key distribution(QKD)system.In this study,we apply the TWCC method to improve the performance of reference-frame-independent quantum key distribution(RFI-QKD),and analyze the influence of the TWCC method on the performance of decoy-state RFI-QKD in both asymptotic and non-asymptotic cases.Our numerical simulation results show that the TWCC method is able to extend the maximal transmission distance from 175 km to 198 km and improve the tolerable bit error rate from 10.48%to 16.75%.At the same time,the performance of RFI-QKD in terms of the secret key rate and maximum transmission distance are still greatly improved when statistical fluctuations are considered.We conclude that RFI-QKD with the TWCC method is of practical interest.展开更多
Measurement-device-independent quantum key distribution (MDI-QKD) is proven to be immune to all the de- tector side channel attacks. With two symmetric quantum channels, the maximal transmission distance can be doub...Measurement-device-independent quantum key distribution (MDI-QKD) is proven to be immune to all the de- tector side channel attacks. With two symmetric quantum channels, the maximal transmission distance can be doubled when compared with the prepare-and-measure QKD. An interesting question is whether the transmission distance can be extended further. In this work, we consider the contributions of the two-way local operations and classical communications to the key generation rate and transmission distance of the MDI-QKD. Our numerical results show that the secure transmission distances are increased by about 12kin and 8 km when the 1 13 and the 2 B steps are implemented, respectively.展开更多
The decoy-state quantum key distribution protocol suggested by Adachi et al. (Phys. Rev. Lett 99 180503 (2007)) is proven to be secure and feasible with current techniques. It owns two attractive merits, i.e., its...The decoy-state quantum key distribution protocol suggested by Adachi et al. (Phys. Rev. Lett 99 180503 (2007)) is proven to be secure and feasible with current techniques. It owns two attractive merits, i.e., its longer secure transmission distance and more convenient operation design. In this paper, we first improve the protocol with the aid of local operation and two-way classical communication (2-LOCC). After our modifications, the secure transmission distance is increased by about 20 km, which will make the protocol more practicable.展开更多
In this paper, we describe an improved cooperative two-way quantum communication scheme that works in a forward-and-backward fashion. In this scheme, partial entanglement analysis based on five-qubit entangled Brown s...In this paper, we describe an improved cooperative two-way quantum communication scheme that works in a forward-and-backward fashion. In this scheme, partial entanglement analysis based on five-qubit entangled Brown state allows for the simultaneous exchange of arbitrary unknown states between Alice and Bob (with the help of trusted Charlie). Security is guaranteed because opposing unknown states are transmitted by performing the suitable recovery operations in a deterministic way or, in the case of irregularities, no results are generated. The current two-way quantum communication scheme can also be extended to transmit arbitrary unknown states. This is done in a probabilistic way by using two-way quantum teleportation based on the generalized Brown-like state.展开更多
Aiming at the energy consumption of long-distance device-to-device(D2D) devices for two-way communications in a cellular network,this paper proposes a strategy that combines two-way relay technology(TWRT) and simultan...Aiming at the energy consumption of long-distance device-to-device(D2D) devices for two-way communications in a cellular network,this paper proposes a strategy that combines two-way relay technology(TWRT) and simultaneous wireless information and power transfer(SWIPT) technology to achieve high energy efficiency(EE) communication.The scheme first establishes a fractional programming problem to maximize EE of D2D,and transforms it into a non-fractional optimization problem that can be solved easily.Then the problem is divided into three sub-problems:power control,power splitting ratios optimization,and relay selection.In order to maximize EE of the D2D pair,the Dinkelbach iterative algorithm is used to optimize the transmitted power of two D2D devices simultaneously;the one-dimensional search algorithm is proposed to optimize power splitting ratios;an improved optimal relay selection scheme based on EE is proposed to select relay.Finally,experiments are carried out on the Matlab simulation platform.The simulation results show that the proposed algorithm has faster convergence.Compared with the one-way relay transmission and fixed relay algorithms,the proposed scheme has higher EE.展开更多
In this paper, we investigate the energy efficiency and spectrum efficiency, including one-hop device-to-device(D2D) communications mode and two-way amplify-and-forward(AF) relaying D2D communications mode in underlay...In this paper, we investigate the energy efficiency and spectrum efficiency, including one-hop device-to-device(D2D) communications mode and two-way amplify-and-forward(AF) relaying D2D communications mode in underlay D2D communications enabled cellular networks. An analysis of average energy efficiency and spectrum efficiency are developed and closed-form expressions are obtained for two types of D2D communications modes under the effect of Rayleigh fading channel, path loss, and co-channel interference. Analytical results are validated through numerical simulations. Based on the simulation, the effects of the interference, the distance between D2D pair and the position of relay node on the energy efficiency and spectrum efficiency of D2D communications are investigated. The optimal D2D transmission powers of these two modes to maximize the energy efficiency are also investigated.展开更多
An estimate-and-forward(EF) scheme for single-input single-output(SISO) and multiple-input multiple-output(MIMO) full-duplex two-way relay networks is proposed and analyzed. The relay estimates the received signal fro...An estimate-and-forward(EF) scheme for single-input single-output(SISO) and multiple-input multiple-output(MIMO) full-duplex two-way relay networks is proposed and analyzed. The relay estimates the received signal from two terminal nodes by a minimum mean squared error(MMSE) estimation and forwards a scaled version of the MMSE estimate to the destination. The proposed EF outperforms conventional amplify-and-forward(AF) and decode-and-forward(DF) across all signal-to-noise ratio(SNR) region. Because its computational complexity is high for relays with a large number of antennas(large MIMO) and/or high order constellations, an approximate EF scheme, called list EF, are thus proposed to reduce the computational complexity. The proposed list EF computes a candidate list for the MMSE estimate by using a sphere decoder, and it approaches the performance of the exact EF relay at a negligible performance loss. The proposed forwarding approach also could be used to other relay networks, such as half-duplex, one-way or massive MIMO relay networks.展开更多
Interference alignment(IA) is one of the promising measures for the multi-user network to manage interference. The rank constraints rank minimization means that interference spans the lowest dimensional subspace and t...Interference alignment(IA) is one of the promising measures for the multi-user network to manage interference. The rank constraints rank minimization means that interference spans the lowest dimensional subspace and the useful signal spans all available spatial dimensions. In order to improve the performance of two-way relay network, we can use rank constrained rank minimization(RCRM) to solve the IA problem. This paper proposes left reweighted nuclear norm minimization-γalgorithm and selective coupling reweighted nuclear norm minimization algorithm to implement interference alignment in two-way relay networks. The left reweighted nuclear norm minimization-γ algorithm is based on reweighted nuclear norm minimization algorithm and has a novel γ choosing rule. The selective coupling reweighted nuclear norm minimization algorithm weighting methods choose according to singular value of interference matrixes. Simulation results show that the proposed algorithms considerably improve the sum rate performance and achieve the higher average achievable multiplexing gain in two-way relay interference networks.展开更多
In this paper, we present a two-way quantum dense key distribution protocol. With double check modes, our scheme is secure regardless of the presence of noises. And with a quantum teleportation process, secret message...In this paper, we present a two-way quantum dense key distribution protocol. With double check modes, our scheme is secure regardless of the presence of noises. And with a quantum teleportation process, secret message can be encoded deterministically even if the quantum channel is highly lossy. Therefore, our scheme can be used in a realistic quantum channel regardless of the presence of noises and channel losses.展开更多
This paper investigates the achievable secrecy rate region of the Gaussian two-way wiretap channel,which describes the simultaneous secure two-way transmission of a confidential message. Through adjusting the time-sha...This paper investigates the achievable secrecy rate region of the Gaussian two-way wiretap channel,which describes the simultaneous secure two-way transmission of a confidential message. Through adjusting the time-sharing factor and the rate at which the random secret key is fed back, the allocation and optimization for the secrecy rates of two-way communication are achieved. Under peak and average power constraints, the achievable secrecy rate regions of the two-way communication are derived respectively.展开更多
In this paper,the logic is developed assuming that all parts of the brain are composed of a combination of modules that basically have the same structure.The feeding behavior of searching for food while avoiding the d...In this paper,the logic is developed assuming that all parts of the brain are composed of a combination of modules that basically have the same structure.The feeding behavior of searching for food while avoiding the dangers of animals in the early stages of evolution is regarded as the basis of time series data processing.The module that performs the processing is presented by a neural network equipped with a learning function based on Hebb's rule,and is called a basic unit.The basic units are arranged in layers,and the information between the layers is bidirectional.This new neural network is an extension of the traditional neural network that has evolved from pattern recognition.The biggest feature is that in the processing of time series data,the activated part changes according to the context structure inherent in the data,and can be mathematically expressed the method of predicting events from the context of learned behavior and utilizing it in best action.展开更多
We propose two novel power control policies for a two-way amplify-and-forward (AF) relaying system,in which each node (two sources and one relay) is assumed to operate under bothminimum and peak power constraints.Thro...We propose two novel power control policies for a two-way amplify-and-forward (AF) relaying system,in which each node (two sources and one relay) is assumed to operate under bothminimum and peak power constraints.Through the exploitation of instantaneous channel gains,the first policy can maximize the sum rate of the system.However,the instantaneous channel gains may be unavailable in a rapid time-varying system,where the first policy is inoperable.Consequently,a robust power control policy which requires only mean channel gains is proposed to maximize the upper bound of the average sum rate,and the properties of this policy are investigated.Simulation results show that,by comparison with the policy in which all the nodes use their peak transmit power,the proposed power control policies can provide considerable system performance improvement.Furthermore,the performance difference between the two proposed policies is negligible when the relay is close to one source.展开更多
In cellular networks, users communicate with each other through their respective base stations(BSs).Conventionally, users are assumed to be in different cells. BSs serve as decode-and-forward(DF) relay nodes to us...In cellular networks, users communicate with each other through their respective base stations(BSs).Conventionally, users are assumed to be in different cells. BSs serve as decode-and-forward(DF) relay nodes to users.In addition to this type of conventional user, we recognize that there are scenarios users who want to communicate with each other are located in the same cell. This gives rise to the scenario of intra-cell communication. In this case, a BS can behave as a two-way relay to achieve information exchange instead of using conventional DF relay.We consider a multi-cell orthogonal frequency division multiple access(OFDMA) network that comprises these two types of users. We are interested in resource allocation between them. Specifically, we jointly optimize subcarrier assignment, subcarrier pairing, and power allocation to maximize the weighted sum rate. We consider the resource allocation problem at BSs when the end users' power is fixed. We solve the problem approximately through Lagrange dual decomposition. Simulation results show that the proposed schemes outperform other existing schemes.展开更多
基金supported in part by the National Key Research and Development Program of China(2019YFB2204701)in part by the National Natural Science Foundation of China(61831006,62022023,and 62250610223)in part by the Big Data Computing Center at Southeast University for numerical calculation.
文摘This article proposes and demonstrates a retrodirective array(RDA)for two-way wireless communication with automatic beam tracking.The proposed RDA is enabled by specifically designed chips made using a domestic complementary metal-oxide semiconductor(CMOS)process.The highly integrated CMOS chip includes a receiving(Rx)chain,a transmitting(Tx)chain,and a unique tracking phaselocked loop(PLL)for the crucial conjugated phase recovery in the RDA.This article also proposes a method to reduce the beam pointing error(BPE)in a conventional RDA.To validate the above ideas simply yet without loss of generality,a 2.4 GHz RDA is demonstrated through two-way communication links between the Rx and Tx chains,and an on-chip quadrature coupler is designed to achieve a nonretrodirective signal suppression of 23 dBc.The experimental results demonstrate that the proposed RDA,which incorporates domestically manufactured low-cost 0.18 lm CMOS chips,is capable of automatically tracking beams covering±40with a reduced BPE.Each CMOS chip in the RDA has a compact size of 4.62 mm^(2) and a low power consumption of 0.15 W.To the best of the authors’knowledge,this is the first research to demonstrate an RDA with a fully customized CMOS chip for wireless communication with automatic beam tracking。
基金supported by the National Natural Science Foundation of China(Grant Nos.61505261,62101597,61605248,and 61675235)the National Key Research and Development Program of China(Grant No.2020YFA0309702)+2 种基金the China Postdoctoral Science Foundation(Grant No.2021M691536)the Natural Science Foundation of Henan Province(Grant Nos.202300410534 and 202300410532)the Anhui Initiative in Quantum Information Technologies.
文摘The data post-processing scheme based on two-way classical communication(TWCC)can improve the tolerable bit error rate and extend the maximal transmission distance when used in a quantum key distribution(QKD)system.In this study,we apply the TWCC method to improve the performance of reference-frame-independent quantum key distribution(RFI-QKD),and analyze the influence of the TWCC method on the performance of decoy-state RFI-QKD in both asymptotic and non-asymptotic cases.Our numerical simulation results show that the TWCC method is able to extend the maximal transmission distance from 175 km to 198 km and improve the tolerable bit error rate from 10.48%to 16.75%.At the same time,the performance of RFI-QKD in terms of the secret key rate and maximum transmission distance are still greatly improved when statistical fluctuations are considered.We conclude that RFI-QKD with the TWCC method is of practical interest.
基金Supported by the National Natural Science Foundation of China under Grant No 61378011the Program for Science and Technology Innovation Research Team in University of Henan Province under Grant No 13IRTSTHN020
文摘Measurement-device-independent quantum key distribution (MDI-QKD) is proven to be immune to all the de- tector side channel attacks. With two symmetric quantum channels, the maximal transmission distance can be doubled when compared with the prepare-and-measure QKD. An interesting question is whether the transmission distance can be extended further. In this work, we consider the contributions of the two-way local operations and classical communications to the key generation rate and transmission distance of the MDI-QKD. Our numerical results show that the secure transmission distances are increased by about 12kin and 8 km when the 1 13 and the 2 B steps are implemented, respectively.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 10905028/A050104)the Natural Science Foundation of Henan Province,China (Grant No. 092300410188)+1 种基金the Science Foundation of Hennan Provincial Education Department (Grant No. 2010A140010)Youth Fund of Luoyang Normal College
文摘The decoy-state quantum key distribution protocol suggested by Adachi et al. (Phys. Rev. Lett 99 180503 (2007)) is proven to be secure and feasible with current techniques. It owns two attractive merits, i.e., its longer secure transmission distance and more convenient operation design. In this paper, we first improve the protocol with the aid of local operation and two-way classical communication (2-LOCC). After our modifications, the secure transmission distance is increased by about 20 km, which will make the protocol more practicable.
基金supported by the National Natural Science Foundation of China(60902044,61172184)the New Century Excellent Talents in University(NCET-11-0510)+1 种基金partly by the World Class University R32-2010-000-20014-0NRFFundamental Research 2010-0020942 NRF,Korea
文摘In this paper, we describe an improved cooperative two-way quantum communication scheme that works in a forward-and-backward fashion. In this scheme, partial entanglement analysis based on five-qubit entangled Brown state allows for the simultaneous exchange of arbitrary unknown states between Alice and Bob (with the help of trusted Charlie). Security is guaranteed because opposing unknown states are transmitted by performing the suitable recovery operations in a deterministic way or, in the case of irregularities, no results are generated. The current two-way quantum communication scheme can also be extended to transmit arbitrary unknown states. This is done in a probabilistic way by using two-way quantum teleportation based on the generalized Brown-like state.
基金Supported by the National Natural Science Foundation of China (No.61561031)。
文摘Aiming at the energy consumption of long-distance device-to-device(D2D) devices for two-way communications in a cellular network,this paper proposes a strategy that combines two-way relay technology(TWRT) and simultaneous wireless information and power transfer(SWIPT) technology to achieve high energy efficiency(EE) communication.The scheme first establishes a fractional programming problem to maximize EE of D2D,and transforms it into a non-fractional optimization problem that can be solved easily.Then the problem is divided into three sub-problems:power control,power splitting ratios optimization,and relay selection.In order to maximize EE of the D2D pair,the Dinkelbach iterative algorithm is used to optimize the transmitted power of two D2D devices simultaneously;the one-dimensional search algorithm is proposed to optimize power splitting ratios;an improved optimal relay selection scheme based on EE is proposed to select relay.Finally,experiments are carried out on the Matlab simulation platform.The simulation results show that the proposed algorithm has faster convergence.Compared with the one-way relay transmission and fixed relay algorithms,the proposed scheme has higher EE.
基金supported by the National Natural Science Foundation of China under Grant U1805262, 61871446, 61671251 and 61701201the Natural Science Foundation of Jiangsu Province under Grant No.BK20170758+2 种基金the Natural Science Foundation for colleges and universities of Jiangsu Province under Grant No.17KJB510011the open research fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2015D10Project of Key Laboratory of Wireless Communications of Jiangsu Province under Grant No.NK214001
文摘In this paper, we investigate the energy efficiency and spectrum efficiency, including one-hop device-to-device(D2D) communications mode and two-way amplify-and-forward(AF) relaying D2D communications mode in underlay D2D communications enabled cellular networks. An analysis of average energy efficiency and spectrum efficiency are developed and closed-form expressions are obtained for two types of D2D communications modes under the effect of Rayleigh fading channel, path loss, and co-channel interference. Analytical results are validated through numerical simulations. Based on the simulation, the effects of the interference, the distance between D2D pair and the position of relay node on the energy efficiency and spectrum efficiency of D2D communications are investigated. The optimal D2D transmission powers of these two modes to maximize the energy efficiency are also investigated.
基金supported in part by the National Natural Science Foundation of China 61501461, 61471269, 61622101 and 61571020the National 973 Project under grant 2013CB336700+2 种基金the National 863 Project under grant SS2015AA011306the National Science Foundation under grant number CNS-1343189 and ECCS-1232305the Early Career Development Award of SKLMCCS (Y3S9021F34)
文摘An estimate-and-forward(EF) scheme for single-input single-output(SISO) and multiple-input multiple-output(MIMO) full-duplex two-way relay networks is proposed and analyzed. The relay estimates the received signal from two terminal nodes by a minimum mean squared error(MMSE) estimation and forwards a scaled version of the MMSE estimate to the destination. The proposed EF outperforms conventional amplify-and-forward(AF) and decode-and-forward(DF) across all signal-to-noise ratio(SNR) region. Because its computational complexity is high for relays with a large number of antennas(large MIMO) and/or high order constellations, an approximate EF scheme, called list EF, are thus proposed to reduce the computational complexity. The proposed list EF computes a candidate list for the MMSE estimate by using a sphere decoder, and it approaches the performance of the exact EF relay at a negligible performance loss. The proposed forwarding approach also could be used to other relay networks, such as half-duplex, one-way or massive MIMO relay networks.
基金supported by the National Science Foundation of China (NO.61271240, 61671253)
文摘Interference alignment(IA) is one of the promising measures for the multi-user network to manage interference. The rank constraints rank minimization means that interference spans the lowest dimensional subspace and the useful signal spans all available spatial dimensions. In order to improve the performance of two-way relay network, we can use rank constrained rank minimization(RCRM) to solve the IA problem. This paper proposes left reweighted nuclear norm minimization-γalgorithm and selective coupling reweighted nuclear norm minimization algorithm to implement interference alignment in two-way relay networks. The left reweighted nuclear norm minimization-γ algorithm is based on reweighted nuclear norm minimization algorithm and has a novel γ choosing rule. The selective coupling reweighted nuclear norm minimization algorithm weighting methods choose according to singular value of interference matrixes. Simulation results show that the proposed algorithms considerably improve the sum rate performance and achieve the higher average achievable multiplexing gain in two-way relay interference networks.
基金Project supported by the National Natural Science Foundation of China (Grant No 10504039).Acknowledgment We thank Qing-yu Cai for useful discussion.
文摘In this paper, we present a two-way quantum dense key distribution protocol. With double check modes, our scheme is secure regardless of the presence of noises. And with a quantum teleportation process, secret message can be encoded deterministically even if the quantum channel is highly lossy. Therefore, our scheme can be used in a realistic quantum channel regardless of the presence of noises and channel losses.
基金supported in part by the National HighTech Research and Development (863) Program (No. ss2015AA011306)the National key Basic Research and Development (973) Program of China (No. 2012CB316000)+1 种基金the Science Fund for Creative Research Groups of NSFC (No. 61321061)Tsinghua University Initiative Scientific Research (No. 2015Z02-3)
文摘This paper investigates the achievable secrecy rate region of the Gaussian two-way wiretap channel,which describes the simultaneous secure two-way transmission of a confidential message. Through adjusting the time-sharing factor and the rate at which the random secret key is fed back, the allocation and optimization for the secrecy rates of two-way communication are achieved. Under peak and average power constraints, the achievable secrecy rate regions of the two-way communication are derived respectively.
文摘In this paper,the logic is developed assuming that all parts of the brain are composed of a combination of modules that basically have the same structure.The feeding behavior of searching for food while avoiding the dangers of animals in the early stages of evolution is regarded as the basis of time series data processing.The module that performs the processing is presented by a neural network equipped with a learning function based on Hebb's rule,and is called a basic unit.The basic units are arranged in layers,and the information between the layers is bidirectional.This new neural network is an extension of the traditional neural network that has evolved from pattern recognition.The biggest feature is that in the processing of time series data,the activated part changes according to the context structure inherent in the data,and can be mathematically expressed the method of predicting events from the context of learned behavior and utilizing it in best action.
基金supported by the Sino-Swedish IMT-Advanced Cooperation Project (No.2008DFA11780)the Canada-China Scientific and Technological Cooperation (No.2010DFA11320)+1 种基金the National Natural Science Foundation of China (Nos.60802033 and 60873190)the National High-Tech R&D Program (863) of China (No.2008AA01Z211)
文摘We propose two novel power control policies for a two-way amplify-and-forward (AF) relaying system,in which each node (two sources and one relay) is assumed to operate under bothminimum and peak power constraints.Through the exploitation of instantaneous channel gains,the first policy can maximize the sum rate of the system.However,the instantaneous channel gains may be unavailable in a rapid time-varying system,where the first policy is inoperable.Consequently,a robust power control policy which requires only mean channel gains is proposed to maximize the upper bound of the average sum rate,and the properties of this policy are investigated.Simulation results show that,by comparison with the policy in which all the nodes use their peak transmit power,the proposed power control policies can provide considerable system performance improvement.Furthermore,the performance difference between the two proposed policies is negligible when the relay is close to one source.
基金Project supported by the Natural Science Foundation of Shandong Province,China(No.ZR2012AQ015)
文摘In cellular networks, users communicate with each other through their respective base stations(BSs).Conventionally, users are assumed to be in different cells. BSs serve as decode-and-forward(DF) relay nodes to users.In addition to this type of conventional user, we recognize that there are scenarios users who want to communicate with each other are located in the same cell. This gives rise to the scenario of intra-cell communication. In this case, a BS can behave as a two-way relay to achieve information exchange instead of using conventional DF relay.We consider a multi-cell orthogonal frequency division multiple access(OFDMA) network that comprises these two types of users. We are interested in resource allocation between them. Specifically, we jointly optimize subcarrier assignment, subcarrier pairing, and power allocation to maximize the weighted sum rate. We consider the resource allocation problem at BSs when the end users' power is fixed. We solve the problem approximately through Lagrange dual decomposition. Simulation results show that the proposed schemes outperform other existing schemes.