We propose a Rate-Distortion (RD) optimized strategy for frame-dropping and scheduling of multi-user conversa- tional and streaming videos. We consider a scenario where conversational and streaming videos share the fo...We propose a Rate-Distortion (RD) optimized strategy for frame-dropping and scheduling of multi-user conversa- tional and streaming videos. We consider a scenario where conversational and streaming videos share the forwarding resources at a network node. Two buffers are setup on the node to temporarily store the packets for these two types of video applications. For streaming video, a big buffer is used as the associated delay constraint of the application is moderate and a very small buffer is used for conversational video to ensure that the forwarding delay of every packet is limited. A scheduler is located behind these two buffers that dynamically assigns transmission slots on the outgoing link to the two buffers. Rate-distortion side information is used to perform RD-optimized frame dropping in case of node overload. Sharing the data rate on the outgoing link between the con- versational and the streaming videos is done either based on the fullness of the two associated buffers or on the mean incoming rates of the respective videos. Simulation results showed that our proposed RD-optimized frame dropping and scheduling ap- proach provides significant improvements in performance over the popular priority-based random dropping (PRD) technique.展开更多
In this paper we discuss the source rate control problem of adapting variable bit-rate (VBR) compressed video over constant bit-rate (CBR) channels. Firstly we formulate it as an optimal control problem of a discr...In this paper we discuss the source rate control problem of adapting variable bit-rate (VBR) compressed video over constant bit-rate (CBR) channels. Firstly we formulate it as an optimal control problem of a discrete linear system with state and control constraints. Then we apply the discrete maximum principle to get the optimal solution. Experimental results are given in the end. Compared with traditional algorithms, the proposed algorithm is suitable for the coder with continuous output rates, and can achieve the better solution. Our algorithm can be used in both off-line and on-line coding.展开更多
The Rate Distortion Optimization(RDO)algorithm in High Efficiency Video Coding(HEVC)has many iterations and a large number of calculations.In order to decrease the calculation time and meet the requirements of fast sw...The Rate Distortion Optimization(RDO)algorithm in High Efficiency Video Coding(HEVC)has many iterations and a large number of calculations.In order to decrease the calculation time and meet the requirements of fast switching of RDO algorithms of different scales,an RDO dynamic reconfigurable structure is proposed.First,the Quantization Parameter(QP)and bit rate values were loaded through an H⁃tree Configurable Network(HCN),and the execution status of the array was detected in real time.When the switching request of the RDO algorithm was detected,the corresponding configuration information was delivered.This self⁃reconfiguration implementation method improved the flexibility and utilization of hardware.Experimental results show that when the control bit width was only increased by 31.25%,the designed configuration network could increase the number of controllable processing units by 32 times,and the execution cycle was 50%lower than the same type of design.Compared with previous RDO algorithm,the RDO algorithm implemented on the reconfigurable array based on the configuration network had an average operating frequency increase of 12.5%and an area reduction of 56.4%.展开更多
Rate control is one of the key factors influencing the multi-view video transmission.However,there is not a rate control algorithm in the existing Joint Multi-view Video Coding Model.In this paper,an efficient rate co...Rate control is one of the key factors influencing the multi-view video transmission.However,there is not a rate control algorithm in the existing Joint Multi-view Video Coding Model.In this paper,an efficient rate control algorithm and a bit allocation strategy for multi-view video coding are proposed.In order to obtain the consistent view quality,a bit allocation model based on the Lagrange optimum algorithm is firstly proposed.Secondly,considering the encoding statistical characteristics of different view types,a view weighting factor is introduced,and it will help improve the precision of bit allocation among views.Compared with the fixed QP control strategy,experiment results show that the proposed algorithm can efficiently control the bit rate and obtain more consistent views,with video visual quality improved.展开更多
Rate control is a key technology in the fields of video coding and transmission, and it has attracted a great attention and has been studied extensively. The TM5 framework of MPEG-2 is a classical rate control algo-ri...Rate control is a key technology in the fields of video coding and transmission, and it has attracted a great attention and has been studied extensively. The TM5 framework of MPEG-2 is a classical rate control algo-rithm and has being widely used. However, it has some underlying drawbacks during practical applications such as the poor rate control precision and high computational complexity. Hence, in this paper, a novel rate-control algorithm based on the TM5 framework is proposed. The drawback of the target bit allocation method of the original TM5 algorithm is firstly analyzed and improved. Then, a new rate-distortion model is incorporated into the rate control algorithm to implement rate prediction to enhance the rate-control precision. Meanwhile, the macro-block (MB) level rate control is adapted to be frame level to reduce the computational complexity. Experiments are conducted and some results are given. Compared with the original TM5 algo-rithm, the improved novel algorithm not only can enhance the rate-control precision but also can reduce the complexity and the fluctuation of decoded image quality.展开更多
The JPEG2000 image compression standard is the powerful encoder which can provide phenomenal rate-control performance. The post-compression rate-distortion(PCRD) algorithm in JPEG2000 is not efficient. It requires enc...The JPEG2000 image compression standard is the powerful encoder which can provide phenomenal rate-control performance. The post-compression rate-distortion(PCRD) algorithm in JPEG2000 is not efficient. It requires encoding all coding passes even though a large contribution of them will not be contained in the final code-stream. Tier-1 encoding in the JPEG2000 standard takes a significant amount of memory and coding time. In this work, a low-complexity rate distortion method for JPEG2000 is proposed. It is relied on a reverse order for the resolution levels and the coding passes. The proposed algorithm encodes only the coding passes contained in the final code-stream and it does not need any post compression rate control part. The computational complexity of proposed algorithm is negligible, making it suitable to compression and attaining a significant performance. Simulations results show that the proposed algorithm obtained the PSNR values are comparable with the optimal PCRD.展开更多
Fine scalability can provide not only precise rate control for constant bitrate (CBR) traffic, but also accurate quality control for variable bitrate (VBR) traffic. Motion JPEG2000 is a codec that can provide fine sca...Fine scalability can provide not only precise rate control for constant bitrate (CBR) traffic, but also accurate quality control for variable bitrate (VBR) traffic. Motion JPEG2000 is a codec that can provide fine scalability with bitstreams. An efficient rate control approach utilizing a single buffer and two kinds of threshold for Motion JPEG2000 under resource constraint was proposed, which can offer good result in the constant quality video.展开更多
The paper focuses on the optimal control of natural resources in mining industry. The purpose is to pro- pose an optimal extraction series of these resources during the lifetime of the Mine's maintenance. Fol- lowing...The paper focuses on the optimal control of natural resources in mining industry. The purpose is to pro- pose an optimal extraction series of these resources during the lifetime of the Mine's maintenance. Fol- lowing the proposed optimal control model, a sensitivity analysis has been performed that includes the interest rate impact on the optimal solution. This study shows that the increasing of the interest rate sti- mulates faster extraction of the resources. The discounting factor induces that the resource has to be extracted faster hut this effect is counterbalanced by the diminishing returns of the annual cash flow. At higher parameters of "alpha" close to one of the power function about 80% from the whole resource will be extracted during the first 4 years of object/mine maintenance. An existence of unique positive root with respect to return of investment has been proposed and proved by two ways: by the "method of chords" and by using specialized software.展开更多
This paper presents an improved rate control method for H.264. First, the scene changes are detected by the average absolute difference of the brightness histograms between the adjacent frames. Then, the bit allocatio...This paper presents an improved rate control method for H.264. First, the scene changes are detected by the average absolute difference of the brightness histograms between the adjacent frames. Then, the bit allocation and quantization parameters are adjusted, using a certain threshold. In addition, the calculation of the mean absolute difference (MAD) is modified in an alternative way, which makes the rate distortion optimization (RDO) more accurate. Extensive simulation results show that the proposed method, compared with G012, can improve the average peak signal-to-noise ratio (PSNR) and moderate the image quality.展开更多
Rate control plays a critical role in achieving perceivable video quality under a variable bit rate,limited buffer sizes and low delay applications.Since a rate control system exhibits non-linear and unpredictable cha...Rate control plays a critical role in achieving perceivable video quality under a variable bit rate,limited buffer sizes and low delay applications.Since a rate control system exhibits non-linear and unpredictable characteristics,it is difficult to establish a very accurate rate-distortion(R-D)model and acquire effective rate control performance.Considering the excellent control ability and low computing complexity of the fuzzy logic in non-linear systems,this paper proposes a bitrate control algorithm based on a fuzzy controller,named the Fuzzy Rate Control Algorithm(FRCA),for All-Intra(AI)and low-delay(LD)video source coding.Contributions of the proposed FRCA mainly consist of four aspects.First,fuzzy logic is adopted to minimize the deviation between the actual and the target buffer size in the hypothetical reference decoder(HRD).Second,a fast lookup table is employed in fuzzy rate control,which reduces computing cost of the control process.Third,an input domain determination scheme is proposed to improve the precision of the fuzzy controller.Fourth,a novel scene change detection is introduced and integrated in the FRCA to adaptively adjust the Group-of-Pictures(GOP)length when the source content fluctuates.The FRCA can be transplanted and implemented in various industry coders.Extensive experiments show that the FRCA has accurate variable bit-rate control ability and maintains a steady buffer size during the encoding processes.Compared with the default configuration encoding under AI and LD,the proposed FRCA can achieve the target bit rates more accurately in various classical encoders.展开更多
This paper proposes an adaptive video pre-processing algorithm for video coding. This algorithm works on the original image before intraor inter-prediction. It adopts Gaussian filter to remove noise and insignificant ...This paper proposes an adaptive video pre-processing algorithm for video coding. This algorithm works on the original image before intraor inter-prediction. It adopts Gaussian filter to remove noise and insignificant features existing in images of video. Detection and restoration of edges are followed to restore the edges which are excessively filtered out in filtered images. Rate-Distortion Optimization (RDO) is employed to decide adaptively whether a processed block or a unprocessed block is coded into bit-streams doe more efficient coding. Our experiment results show that the algorithm achieves good coding performances on both subjective and objective aspects. In addition, the proposed pre-processing algorithm is transparent to decoder, and thus can be compliant with any video coding standards without modifying the decoder.展开更多
Many modern video encoders use the Lagrangian rate-distortion optimization (RDO) algorithm for mode deci- sions during the compression procedure. For each encoding stage, this approach involves minimizing a cost, wh...Many modern video encoders use the Lagrangian rate-distortion optimization (RDO) algorithm for mode deci- sions during the compression procedure. For each encoding stage, this approach involves minimizing a cost, which is a function of rate, distortion and a multiplier called Lambda. This paper proposes to improve the RDO process by applying two modifications. The first modification is to increase the ac- curacy of rate estimation, which is achieved by computing a non-integer number of bits for arithmetic coding of the syntax elements. This leads to a more accurate cost computation and therefore a better mode decision. The second modification is to search and adjust the value of Lambda based on the char- acteristics of each coding stage. For the encoder used, this paper proposes to search multiple values of Lambda for the intra-4x4 mode decision. Moreover, a simple shift in Lambda value is proposed for motion estimation. Each of these modi- fications offers a certain gain in RDO performance, and, when all are combined, an average bit-rate saving of up to 7.0% can be achieved for the H.264/AVC codec while the same concept is applicable to the H.265/HEVC codec as well. The extra added complexity is contained to a certain level, and is also adjustable according to the processing resources available.展开更多
在R-λ帧内码控中,提出基于卷积神经网络(Convolutional Neural Networks,CNN)的最佳比特分配和最优拉格朗日因子λ选择。首先,探索编码树单元(Coding Tree Unit,CTU)的码率与失真(Rate-Distortion,R-D)及码率与拉格朗日因子λ(Rate-λ...在R-λ帧内码控中,提出基于卷积神经网络(Convolutional Neural Networks,CNN)的最佳比特分配和最优拉格朗日因子λ选择。首先,探索编码树单元(Coding Tree Unit,CTU)的码率与失真(Rate-Distortion,R-D)及码率与拉格朗日因子λ(Rate-λ,R-λ)的关系特性,设计具有四输出的CNN预测R-D和R-λ曲线的关键参数;然后,建立帧级λ和目标码率的优化方程,反演得到最佳CTU码率分配;最后,根据CTU码率分配和先知的R-λ曲线,得到最优CTU级λ。实验表明,算法在保持4.76%控制精度下,比VTM13.0默认码控算法提高0.31 dB的编码质量。展开更多
In vehicular Ad-hoc networks (VANETs), beacon message is designed for the purpose of periodically broadcasting the status information (velocity, direction, etc.), which enable neighbor awareness and support some s...In vehicular Ad-hoc networks (VANETs), beacon message is designed for the purpose of periodically broadcasting the status information (velocity, direction, etc.), which enable neighbor awareness and support some safety applications. However, under high density scenarios, fixed rate beaconing can cause severe congestion and lower the deliver rate of beacons and other kinds of messages. In this paper, we describe beaconing rate control approach with an one-dimensional Markov model, and based on this, an optimized beacon rate control scheme is proposed which aims to mitigate the congestion and maximize the deliver efficiency of beaconing. Analytical and simulation results show that our proposed scheme can achieve higher adaptability and beaconing efficiency compared with other schemes in various environments.展开更多
The optimal decay rate problem is considered for boundary control system modeling by a flexible structure consisting of a Eular-Bernoulli beam. Controls are a bending moment in proportion to angular velocity and a she...The optimal decay rate problem is considered for boundary control system modeling by a flexible structure consisting of a Eular-Bernoulli beam. Controls are a bending moment in proportion to angular velocity and a shear force in proportion to velocity. A sensitivity asymptotic analysis of the system's eigenvalues and eigenfunctions is set up. It is proved that, for every 0<K 2<+∞ and 0<-K 1<+∞, all the generalized eigenfunctions of form a Riesz basis ofV×H, and the optimal exponential decay rate can be obtained from the spectrum of the system.展开更多
基金Project (No. STE1093/1-1) supported by the German ResearchFoundation, Germany
文摘We propose a Rate-Distortion (RD) optimized strategy for frame-dropping and scheduling of multi-user conversa- tional and streaming videos. We consider a scenario where conversational and streaming videos share the forwarding resources at a network node. Two buffers are setup on the node to temporarily store the packets for these two types of video applications. For streaming video, a big buffer is used as the associated delay constraint of the application is moderate and a very small buffer is used for conversational video to ensure that the forwarding delay of every packet is limited. A scheduler is located behind these two buffers that dynamically assigns transmission slots on the outgoing link to the two buffers. Rate-distortion side information is used to perform RD-optimized frame dropping in case of node overload. Sharing the data rate on the outgoing link between the con- versational and the streaming videos is done either based on the fullness of the two associated buffers or on the mean incoming rates of the respective videos. Simulation results showed that our proposed RD-optimized frame dropping and scheduling ap- proach provides significant improvements in performance over the popular priority-based random dropping (PRD) technique.
文摘In this paper we discuss the source rate control problem of adapting variable bit-rate (VBR) compressed video over constant bit-rate (CBR) channels. Firstly we formulate it as an optimal control problem of a discrete linear system with state and control constraints. Then we apply the discrete maximum principle to get the optimal solution. Experimental results are given in the end. Compared with traditional algorithms, the proposed algorithm is suitable for the coder with continuous output rates, and can achieve the better solution. Our algorithm can be used in both off-line and on-line coding.
基金Sponsored by the National Natural Science Foundation of China(Grant Nos.61834005,61772417,61802304,61602377,and 61634004)the Shaanxi Province Coordination Innovation Project of Science and Technology(Grant No.2016KTZDGY02-04-02)+1 种基金the Shaanxi Provincial Key R&D Plan(Grant No.2017GY-060)the Shaanxi International Science and Technology Cooperation Program(Grant No.2018KW-006).
文摘The Rate Distortion Optimization(RDO)algorithm in High Efficiency Video Coding(HEVC)has many iterations and a large number of calculations.In order to decrease the calculation time and meet the requirements of fast switching of RDO algorithms of different scales,an RDO dynamic reconfigurable structure is proposed.First,the Quantization Parameter(QP)and bit rate values were loaded through an H⁃tree Configurable Network(HCN),and the execution status of the array was detected in real time.When the switching request of the RDO algorithm was detected,the corresponding configuration information was delivered.This self⁃reconfiguration implementation method improved the flexibility and utilization of hardware.Experimental results show that when the control bit width was only increased by 31.25%,the designed configuration network could increase the number of controllable processing units by 32 times,and the execution cycle was 50%lower than the same type of design.Compared with previous RDO algorithm,the RDO algorithm implemented on the reconfigurable array based on the configuration network had an average operating frequency increase of 12.5%and an area reduction of 56.4%.
基金supported by National Natural Science Foundation of China under Grants No. 61071166,No. 61001152 and No. 61071091
文摘Rate control is one of the key factors influencing the multi-view video transmission.However,there is not a rate control algorithm in the existing Joint Multi-view Video Coding Model.In this paper,an efficient rate control algorithm and a bit allocation strategy for multi-view video coding are proposed.In order to obtain the consistent view quality,a bit allocation model based on the Lagrange optimum algorithm is firstly proposed.Secondly,considering the encoding statistical characteristics of different view types,a view weighting factor is introduced,and it will help improve the precision of bit allocation among views.Compared with the fixed QP control strategy,experiment results show that the proposed algorithm can efficiently control the bit rate and obtain more consistent views,with video visual quality improved.
文摘Rate control is a key technology in the fields of video coding and transmission, and it has attracted a great attention and has been studied extensively. The TM5 framework of MPEG-2 is a classical rate control algo-rithm and has being widely used. However, it has some underlying drawbacks during practical applications such as the poor rate control precision and high computational complexity. Hence, in this paper, a novel rate-control algorithm based on the TM5 framework is proposed. The drawback of the target bit allocation method of the original TM5 algorithm is firstly analyzed and improved. Then, a new rate-distortion model is incorporated into the rate control algorithm to implement rate prediction to enhance the rate-control precision. Meanwhile, the macro-block (MB) level rate control is adapted to be frame level to reduce the computational complexity. Experiments are conducted and some results are given. Compared with the original TM5 algo-rithm, the improved novel algorithm not only can enhance the rate-control precision but also can reduce the complexity and the fluctuation of decoded image quality.
文摘The JPEG2000 image compression standard is the powerful encoder which can provide phenomenal rate-control performance. The post-compression rate-distortion(PCRD) algorithm in JPEG2000 is not efficient. It requires encoding all coding passes even though a large contribution of them will not be contained in the final code-stream. Tier-1 encoding in the JPEG2000 standard takes a significant amount of memory and coding time. In this work, a low-complexity rate distortion method for JPEG2000 is proposed. It is relied on a reverse order for the resolution levels and the coding passes. The proposed algorithm encodes only the coding passes contained in the final code-stream and it does not need any post compression rate control part. The computational complexity of proposed algorithm is negligible, making it suitable to compression and attaining a significant performance. Simulations results show that the proposed algorithm obtained the PSNR values are comparable with the optimal PCRD.
文摘Fine scalability can provide not only precise rate control for constant bitrate (CBR) traffic, but also accurate quality control for variable bitrate (VBR) traffic. Motion JPEG2000 is a codec that can provide fine scalability with bitstreams. An efficient rate control approach utilizing a single buffer and two kinds of threshold for Motion JPEG2000 under resource constraint was proposed, which can offer good result in the constant quality video.
文摘The paper focuses on the optimal control of natural resources in mining industry. The purpose is to pro- pose an optimal extraction series of these resources during the lifetime of the Mine's maintenance. Fol- lowing the proposed optimal control model, a sensitivity analysis has been performed that includes the interest rate impact on the optimal solution. This study shows that the increasing of the interest rate sti- mulates faster extraction of the resources. The discounting factor induces that the resource has to be extracted faster hut this effect is counterbalanced by the diminishing returns of the annual cash flow. At higher parameters of "alpha" close to one of the power function about 80% from the whole resource will be extracted during the first 4 years of object/mine maintenance. An existence of unique positive root with respect to return of investment has been proposed and proved by two ways: by the "method of chords" and by using specialized software.
基金Supported by the National Natural Science Foundation of China (60372057)
文摘This paper presents an improved rate control method for H.264. First, the scene changes are detected by the average absolute difference of the brightness histograms between the adjacent frames. Then, the bit allocation and quantization parameters are adjusted, using a certain threshold. In addition, the calculation of the mean absolute difference (MAD) is modified in an alternative way, which makes the rate distortion optimization (RDO) more accurate. Extensive simulation results show that the proposed method, compared with G012, can improve the average peak signal-to-noise ratio (PSNR) and moderate the image quality.
基金supported by ZTE Industry-Academia-Research Cooperation Funds under Grant No.CON1503180004the Postdoctoral Science Foundation of China under Gant No.2014M552342the Foundation of Science and Technology Department of Sichuan Province,China under Grant No.2014GZ0005
文摘Rate control plays a critical role in achieving perceivable video quality under a variable bit rate,limited buffer sizes and low delay applications.Since a rate control system exhibits non-linear and unpredictable characteristics,it is difficult to establish a very accurate rate-distortion(R-D)model and acquire effective rate control performance.Considering the excellent control ability and low computing complexity of the fuzzy logic in non-linear systems,this paper proposes a bitrate control algorithm based on a fuzzy controller,named the Fuzzy Rate Control Algorithm(FRCA),for All-Intra(AI)and low-delay(LD)video source coding.Contributions of the proposed FRCA mainly consist of four aspects.First,fuzzy logic is adopted to minimize the deviation between the actual and the target buffer size in the hypothetical reference decoder(HRD).Second,a fast lookup table is employed in fuzzy rate control,which reduces computing cost of the control process.Third,an input domain determination scheme is proposed to improve the precision of the fuzzy controller.Fourth,a novel scene change detection is introduced and integrated in the FRCA to adaptively adjust the Group-of-Pictures(GOP)length when the source content fluctuates.The FRCA can be transplanted and implemented in various industry coders.Extensive experiments show that the FRCA has accurate variable bit-rate control ability and maintains a steady buffer size during the encoding processes.Compared with the default configuration encoding under AI and LD,the proposed FRCA can achieve the target bit rates more accurately in various classical encoders.
文摘This paper proposes an adaptive video pre-processing algorithm for video coding. This algorithm works on the original image before intraor inter-prediction. It adopts Gaussian filter to remove noise and insignificant features existing in images of video. Detection and restoration of edges are followed to restore the edges which are excessively filtered out in filtered images. Rate-Distortion Optimization (RDO) is employed to decide adaptively whether a processed block or a unprocessed block is coded into bit-streams doe more efficient coding. Our experiment results show that the algorithm achieves good coding performances on both subjective and objective aspects. In addition, the proposed pre-processing algorithm is transparent to decoder, and thus can be compliant with any video coding standards without modifying the decoder.
文摘Many modern video encoders use the Lagrangian rate-distortion optimization (RDO) algorithm for mode deci- sions during the compression procedure. For each encoding stage, this approach involves minimizing a cost, which is a function of rate, distortion and a multiplier called Lambda. This paper proposes to improve the RDO process by applying two modifications. The first modification is to increase the ac- curacy of rate estimation, which is achieved by computing a non-integer number of bits for arithmetic coding of the syntax elements. This leads to a more accurate cost computation and therefore a better mode decision. The second modification is to search and adjust the value of Lambda based on the char- acteristics of each coding stage. For the encoder used, this paper proposes to search multiple values of Lambda for the intra-4x4 mode decision. Moreover, a simple shift in Lambda value is proposed for motion estimation. Each of these modi- fications offers a certain gain in RDO performance, and, when all are combined, an average bit-rate saving of up to 7.0% can be achieved for the H.264/AVC codec while the same concept is applicable to the H.265/HEVC codec as well. The extra added complexity is contained to a certain level, and is also adjustable according to the processing resources available.
基金supported by the National Natural Science Foundation of China (61171111)the Natural Science Foundation Project of CQ CSTC (CSTC2011jj A40046)the Science and Technology Research Projects of Chongqing Municipal Education Commission (KJ120524)
文摘In vehicular Ad-hoc networks (VANETs), beacon message is designed for the purpose of periodically broadcasting the status information (velocity, direction, etc.), which enable neighbor awareness and support some safety applications. However, under high density scenarios, fixed rate beaconing can cause severe congestion and lower the deliver rate of beacons and other kinds of messages. In this paper, we describe beaconing rate control approach with an one-dimensional Markov model, and based on this, an optimized beacon rate control scheme is proposed which aims to mitigate the congestion and maximize the deliver efficiency of beaconing. Analytical and simulation results show that our proposed scheme can achieve higher adaptability and beaconing efficiency compared with other schemes in various environments.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 69674011, 19671054)Science Foundation of Shanxi University.
文摘The optimal decay rate problem is considered for boundary control system modeling by a flexible structure consisting of a Eular-Bernoulli beam. Controls are a bending moment in proportion to angular velocity and a shear force in proportion to velocity. A sensitivity asymptotic analysis of the system's eigenvalues and eigenfunctions is set up. It is proved that, for every 0<K 2<+∞ and 0<-K 1<+∞, all the generalized eigenfunctions of form a Riesz basis ofV×H, and the optimal exponential decay rate can be obtained from the spectrum of the system.