The encoding/decoding scheme based on Fiber Bragg Grating (FBG) for Optical Code Division Multiple Access (OCDMA) system is analyzed and the whole process from transmitting end to receiving end is researched in detail...The encoding/decoding scheme based on Fiber Bragg Grating (FBG) for Optical Code Division Multiple Access (OCDMA) system is analyzed and the whole process from transmitting end to receiving end is researched in detail. The mathematical mode including signal transmission, summing, receiving and recovering are established respectively. One of the main sources of Bit Error Rate (BER) of OCDMA system based on FBGs is the unevenness of signal power spectrum, which leads to the chip powers unequal with each other. The Signal to Interfere Ratio (SIR) and BER performance of the system are studied and simulated at the case with uneven distribution of chips' powers.展开更多
Quantum key distribution is increasingly transitioning toward network applications,necessitating advancements in system performance,including photonic integration for compact designs,enhanced stability against environ...Quantum key distribution is increasingly transitioning toward network applications,necessitating advancements in system performance,including photonic integration for compact designs,enhanced stability against environmental disturbances,higher key rates,and improved efficiency.In this letter,we propose an orthogonal polarization exchange reflector Michelson interferometer model to address quantum channel disturbances caused by environmental factors.Based on this model,we designed a Sagnac reflector-Michelson interferometer decoder and verified its performance through an interference system.The interference fringe visibility exceeded 98%across all four coding phases at 625 MHz.These results indicate that the decoder effectively mitigates environmental interference while supporting high-speed modulation frequencies.In addition,the proposed anti-interference decoder,which does not rely on magneto-optical devices,is well-suited for photonic integration,aligning with the development trajectory for next-generation quantum communication devices.展开更多
In this paper,an improved error-rate sliding window decoder is proposed for spatially coupled low-density parity-check(SC-LDPC)codes.For the conventional sliding window decoder,the message retention mechanism causes u...In this paper,an improved error-rate sliding window decoder is proposed for spatially coupled low-density parity-check(SC-LDPC)codes.For the conventional sliding window decoder,the message retention mechanism causes unreliable messages along the edges of belief propagation(BP)decoding in the current window to be kept for subsequent window decoding.To improve the reliability of the retained messages during the window transition,a reliable termination method is embedded,where the retained messages undergo more reliable parity checks.Additionally,decoding failure is unavoidable and even causes error propagation when the number of errors exceeds the error-correcting capability of the window.To mitigate this problem,a channel value reuse mechanism is designed,where the received channel values are utilized to reinitialize the window.Furthermore,considering the complexity and performance of decoding,a feasible sliding optimized window decoding(SOWD)scheme is introduced.Finally,simulation results confirm the superior performance of the proposed SOWD scheme in both the waterfall and error floor regions.This work has great potential in the applications of wireless optical communication and fiber optic communication.展开更多
Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in cu...Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution.Therefore,quantum error correction technology is crucial to achieving reliable quantum computing.In this work,we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors.However,errors can occur not only in data qubits but also in syndrome qubits,and different types of errors may generate the same syndromes,complicating the decoding task and creating a need for more efficient decoding methods.To address this challenge,we used a transformer decoder based on an attention mechanism.By mapping the surface code lattice,the decoder performs a self-attention process on all input syndromes,thereby obtaining a global receptive field.The performance of the decoder was evaluated under a phenomenological error model.Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%.Additionally,we obtained decoding thresholds of 5%and 6.05%at maximum code distances of 7 and 9,respectively.These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.展开更多
Rail surface damage is a critical component of high-speed railway infrastructure,directly affecting train operational stability and safety.Existing methods face limitations in accuracy and speed for small-sample,multi...Rail surface damage is a critical component of high-speed railway infrastructure,directly affecting train operational stability and safety.Existing methods face limitations in accuracy and speed for small-sample,multi-category,and multi-scale target segmentation tasks.To address these challenges,this paper proposes Pyramid-MixNet,an intelligent segmentation model for high-speed rail surface damage,leveraging dataset construction and expansion alongside a feature pyramid-based encoder-decoder network with multi-attention mechanisms.The encoding net-work integrates Spatial Reduction Masked Multi-Head Attention(SRMMHA)to enhance global feature extraction while reducing trainable parameters.The decoding network incorporates Mix-Attention(MA),enabling multi-scale structural understanding and cross-scale token group correlation learning.Experimental results demonstrate that the proposed method achieves 62.17%average segmentation accuracy,80.28%Damage Dice Coefficient,and 56.83 FPS,meeting real-time detection requirements.The model’s high accuracy and scene adaptability significantly improve the detection of small-scale and complex multi-scale rail damage,offering practical value for real-time monitoring in high-speed railway maintenance systems.展开更多
With the rapid development of low altitude economic industry,low altitude adhoc network technology has been getting more and more intensive attention.In the adhoc network protocol designed in this paper,the convolutio...With the rapid development of low altitude economic industry,low altitude adhoc network technology has been getting more and more intensive attention.In the adhoc network protocol designed in this paper,the convolutional code used is(3,1,7),and the design of a low power Viterbi decoder adapted to multi-rate variations is proposed.In the traditional Viterbi decoding method,the high complexity of path metric(PM)accumulation and Euclidean distance computation leads to the problems of low efficiency and large storage resources in the decoder.In this paper,an improved add compare select(ACS)algorithm,a generalized formula for branch metric(BM)based on Manhattan distance,and a method to reduce the accumulated PM for different Viterbi decoders are put forward.A simulation environment based on Vivado and Matlab to verify the accuracy and effectiveness of the proposed Viterbi decoder is also established.The experimental results show that the total power consumption is reduced by 15.58%while the decoding accuracy of the Viterbi decoder is guaranteed,which meets the design requirements of a low power Viterbi decoder.展开更多
Medical image segmentation has witnessed rapid advancements with the emergence of encoder-decoder based methods.In the encoder-decoder structure,the primary goal of the decoding phase is not only to restore feature ma...Medical image segmentation has witnessed rapid advancements with the emergence of encoder-decoder based methods.In the encoder-decoder structure,the primary goal of the decoding phase is not only to restore feature map resolution,but also to mitigate the loss of feature information incurred during the encoding phase.However,this approach gives rise to a challenge:multiple up-sampling operations in the decoder segment result in the loss of feature information.To address this challenge,we propose a novel network that removes the decoding structure to reduce feature information loss(CBL-Net).In particular,we introduce a Parallel Pooling Module(PPM)to counteract the feature information loss stemming from conventional and pooling operations during the encoding stage.Furthermore,we incorporate a Multiplexed Dilation Convolution(MDC)module to expand the network's receptive field.Also,although we have removed the decoding stage,we still need to recover the feature map resolution.Therefore,we introduced the Global Feature Recovery(GFR)module.It uses attention mechanism for the image feature map resolution recovery,which can effectively reduce the loss of feature information.We conduct extensive experimental evaluations on three publicly available medical image segmentation datasets:DRIVE,CHASEDB and MoNuSeg datasets.Experimental results show that our proposed network outperforms state-of-the-art methods in medical image segmentation.In addition,it achieves higher efficiency than the current network of coding and decoding structures by eliminating the decoding component.展开更多
This paper presents a software turbo decoder on graphics processing units(GPU).Unlike previous works,the proposed decoding architecture for turbo codes mainly focuses on the Consultative Committee for Space Data Syste...This paper presents a software turbo decoder on graphics processing units(GPU).Unlike previous works,the proposed decoding architecture for turbo codes mainly focuses on the Consultative Committee for Space Data Systems(CCSDS)standard.However,the information frame lengths of the CCSDS turbo codes are not suitable for flexible sub-frame parallelism design.To mitigate this issue,we propose a padding method that inserts several bits before the information frame header.To obtain low-latency performance and high resource utilization,two-level intra-frame parallelisms and an efficient data structure are considered.The presented Max-Log-Map decoder can be adopted to decode the Long Term Evolution(LTE)turbo codes with only small modifications.The proposed CCSDS turbo decoder at 10 iterations on NVIDIA RTX3070 achieves about 150 Mbps and 50Mbps throughputs for the code rates 1/6 and 1/2,respectively.展开更多
In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete mem...In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.展开更多
A global optimization algorithm （GOA） for parallel Chien search circuit in Reed-Solomon （RS） （255,239） decoder is presented. By finding out the common modulo 2 additions within groups of Galois field （GF） mult...A global optimization algorithm （GOA） for parallel Chien search circuit in Reed-Solomon （RS） （255,239） decoder is presented. By finding out the common modulo 2 additions within groups of Galois field （GF） multipliers and pre-computing the common items, the GOA can reduce the number of XOR gates efficiently and thus reduce the circuit area. Different from other local optimization algorithms, the GOA is a global one. When there are more than one maximum matches at a time, the best match choice in the GOA has the least impact on the final result by only choosing the pair with the smallest relational value instead of choosing a pair randomly. The results show that the area of parallel Chien search circuits can be reduced by 51% compared to the direct implementation when the group-based GOA is used for GF multipliers and by 26% if applying the GOA to GF multipliers separately. This optimization scheme can be widely used in general parallel architecture in which many GF multipliers are involved.展开更多
The first domestic total dose hardened 2μm partially depleted silicon-on-insulator （PDSOI） CMOS 3-line to 8- line decoder fabricated in SIMOX is demonstrated. The radiation performance is characterized by transisto...The first domestic total dose hardened 2μm partially depleted silicon-on-insulator （PDSOI） CMOS 3-line to 8- line decoder fabricated in SIMOX is demonstrated. The radiation performance is characterized by transistor threshold voltage shifts,circuit static leakage currents,and I-V curves as a function of total dose up to 3× 10^5rad（Si）. The worst case threshold voltage shifts of the front channels are less than 20mV for nMOS transistors at 3 × 10^5rad（Si） and follow-up irradiation and less than 70mV for the pMOS transistors. Furthermore, no significant radiation induced leakage currents and functional degeneration are observed.展开更多
A new encoder/decoder scheme of OCDMA based on waveguide is proposed in this paper. The principle as well as the structure of waveguide encoder/decoder is given. It can be seen that all optical OCDMA encoder/...A new encoder/decoder scheme of OCDMA based on waveguide is proposed in this paper. The principle as well as the structure of waveguide encoder/decoder is given. It can be seen that all optical OCDMA encoder/decoder can be realized by the proposed scheme of the waveguide encoder/decoder. It can also make the OCDMA encoder/decoder integrated easily and the access controlled easily. The system based on this scheme can work under the entirely asynchronous condition.展开更多
We report the LPG pair device that can be used as a pulse duplicator or an OCDMA encoder/decoder. Due to the ring core region of dispersion compensating fiber (DCF), we can shorten the device length by a third and obt...We report the LPG pair device that can be used as a pulse duplicator or an OCDMA encoder/decoder. Due to the ring core region of dispersion compensating fiber (DCF), we can shorten the device length by a third and obtain surrounding insensitive LPG devices.展开更多
A modified Benes network is proposed to be used as an optimal shuffle network in worldwide interoperability for microwave access （WiMAX） low density parity check （LDPC） decoders, When the size of the input is not ...A modified Benes network is proposed to be used as an optimal shuffle network in worldwide interoperability for microwave access （WiMAX） low density parity check （LDPC） decoders, When the size of the input is not a power of two, the modified Benes network can achieve the most optimal performance. This modified Benes network is non-blocking and can perform any sorts of permutations, so it can support 19 modes specified in the WiMAX system. Furthermore, an efficient algorithm to generate the control signals for all the 2 × 2 switches in this network is derived, which can reduce the hardware complexity and overall latency of the modified Benes network. Synthesis results show that the proposed control signal generator can save 25.4% chip area and the overall network latency can be reduced by 36. 2%.展开更多
基金Supported by the Natural Science Research Foundation of Jiangsu Higher-Learning Insti-tution (No.04jkb510057).
文摘The encoding/decoding scheme based on Fiber Bragg Grating (FBG) for Optical Code Division Multiple Access (OCDMA) system is analyzed and the whole process from transmitting end to receiving end is researched in detail. The mathematical mode including signal transmission, summing, receiving and recovering are established respectively. One of the main sources of Bit Error Rate (BER) of OCDMA system based on FBGs is the unevenness of signal power spectrum, which leads to the chip powers unequal with each other. The Signal to Interfere Ratio (SIR) and BER performance of the system are studied and simulated at the case with uneven distribution of chips' powers.
基金supported by the National Natural Science Foundation of China under Grant No.62001440。
文摘Quantum key distribution is increasingly transitioning toward network applications,necessitating advancements in system performance,including photonic integration for compact designs,enhanced stability against environmental disturbances,higher key rates,and improved efficiency.In this letter,we propose an orthogonal polarization exchange reflector Michelson interferometer model to address quantum channel disturbances caused by environmental factors.Based on this model,we designed a Sagnac reflector-Michelson interferometer decoder and verified its performance through an interference system.The interference fringe visibility exceeded 98%across all four coding phases at 625 MHz.These results indicate that the decoder effectively mitigates environmental interference while supporting high-speed modulation frequencies.In addition,the proposed anti-interference decoder,which does not rely on magneto-optical devices,is well-suited for photonic integration,aligning with the development trajectory for next-generation quantum communication devices.
基金supported by the National Natural Science Foundation of China (No.62275193)。
文摘In this paper,an improved error-rate sliding window decoder is proposed for spatially coupled low-density parity-check(SC-LDPC)codes.For the conventional sliding window decoder,the message retention mechanism causes unreliable messages along the edges of belief propagation(BP)decoding in the current window to be kept for subsequent window decoding.To improve the reliability of the retained messages during the window transition,a reliable termination method is embedded,where the retained messages undergo more reliable parity checks.Additionally,decoding failure is unavoidable and even causes error propagation when the number of errors exceeds the error-correcting capability of the window.To mitigate this problem,a channel value reuse mechanism is designed,where the received channel values are utilized to reinitialize the window.Furthermore,considering the complexity and performance of decoding,a feasible sliding optimized window decoding(SOWD)scheme is introduced.Finally,simulation results confirm the superior performance of the proposed SOWD scheme in both the waterfall and error floor regions.This work has great potential in the applications of wireless optical communication and fiber optic communication.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021MF049)Joint Fund of Natural Science Foundation of Shandong Province(Grant Nos.ZR2022LLZ012 and ZR2021LLZ001)the Key R&D Program of Shandong Province,China(Grant No.2023CXGC010901)。
文摘Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution.Therefore,quantum error correction technology is crucial to achieving reliable quantum computing.In this work,we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors.However,errors can occur not only in data qubits but also in syndrome qubits,and different types of errors may generate the same syndromes,complicating the decoding task and creating a need for more efficient decoding methods.To address this challenge,we used a transformer decoder based on an attention mechanism.By mapping the surface code lattice,the decoder performs a self-attention process on all input syndromes,thereby obtaining a global receptive field.The performance of the decoder was evaluated under a phenomenological error model.Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%.Additionally,we obtained decoding thresholds of 5%and 6.05%at maximum code distances of 7 and 9,respectively.These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.
基金supported in part by the National Natural Science Foundation of China under Grant 6226070954Jiangxi Provincial Key R&D Programme under Grant 20244BBG73002.
文摘Rail surface damage is a critical component of high-speed railway infrastructure,directly affecting train operational stability and safety.Existing methods face limitations in accuracy and speed for small-sample,multi-category,and multi-scale target segmentation tasks.To address these challenges,this paper proposes Pyramid-MixNet,an intelligent segmentation model for high-speed rail surface damage,leveraging dataset construction and expansion alongside a feature pyramid-based encoder-decoder network with multi-attention mechanisms.The encoding net-work integrates Spatial Reduction Masked Multi-Head Attention(SRMMHA)to enhance global feature extraction while reducing trainable parameters.The decoding network incorporates Mix-Attention(MA),enabling multi-scale structural understanding and cross-scale token group correlation learning.Experimental results demonstrate that the proposed method achieves 62.17%average segmentation accuracy,80.28%Damage Dice Coefficient,and 56.83 FPS,meeting real-time detection requirements.The model’s high accuracy and scene adaptability significantly improve the detection of small-scale and complex multi-scale rail damage,offering practical value for real-time monitoring in high-speed railway maintenance systems.
基金Supported by the National Natural Science Foundation of China(No.62103257).
文摘With the rapid development of low altitude economic industry,low altitude adhoc network technology has been getting more and more intensive attention.In the adhoc network protocol designed in this paper,the convolutional code used is(3,1,7),and the design of a low power Viterbi decoder adapted to multi-rate variations is proposed.In the traditional Viterbi decoding method,the high complexity of path metric(PM)accumulation and Euclidean distance computation leads to the problems of low efficiency and large storage resources in the decoder.In this paper,an improved add compare select(ACS)algorithm,a generalized formula for branch metric(BM)based on Manhattan distance,and a method to reduce the accumulated PM for different Viterbi decoders are put forward.A simulation environment based on Vivado and Matlab to verify the accuracy and effectiveness of the proposed Viterbi decoder is also established.The experimental results show that the total power consumption is reduced by 15.58%while the decoding accuracy of the Viterbi decoder is guaranteed,which meets the design requirements of a low power Viterbi decoder.
基金funded by the National Key Research and Development Program of China(Grant 2020YFB1708900)the Fundamental Research Funds for the Central Universities(Grant No.B220201044).
文摘Medical image segmentation has witnessed rapid advancements with the emergence of encoder-decoder based methods.In the encoder-decoder structure,the primary goal of the decoding phase is not only to restore feature map resolution,but also to mitigate the loss of feature information incurred during the encoding phase.However,this approach gives rise to a challenge:multiple up-sampling operations in the decoder segment result in the loss of feature information.To address this challenge,we propose a novel network that removes the decoding structure to reduce feature information loss(CBL-Net).In particular,we introduce a Parallel Pooling Module(PPM)to counteract the feature information loss stemming from conventional and pooling operations during the encoding stage.Furthermore,we incorporate a Multiplexed Dilation Convolution(MDC)module to expand the network's receptive field.Also,although we have removed the decoding stage,we still need to recover the feature map resolution.Therefore,we introduced the Global Feature Recovery(GFR)module.It uses attention mechanism for the image feature map resolution recovery,which can effectively reduce the loss of feature information.We conduct extensive experimental evaluations on three publicly available medical image segmentation datasets:DRIVE,CHASEDB and MoNuSeg datasets.Experimental results show that our proposed network outperforms state-of-the-art methods in medical image segmentation.In addition,it achieves higher efficiency than the current network of coding and decoding structures by eliminating the decoding component.
基金supported by the Fundamental Research Funds for the Central Universities(FRF-TP20-062A1)Guangdong Basic and Applied Basic Research Foundation(2021A1515110070)。
文摘This paper presents a software turbo decoder on graphics processing units(GPU).Unlike previous works,the proposed decoding architecture for turbo codes mainly focuses on the Consultative Committee for Space Data Systems(CCSDS)standard.However,the information frame lengths of the CCSDS turbo codes are not suitable for flexible sub-frame parallelism design.To mitigate this issue,we propose a padding method that inserts several bits before the information frame header.To obtain low-latency performance and high resource utilization,two-level intra-frame parallelisms and an efficient data structure are considered.The presented Max-Log-Map decoder can be adopted to decode the Long Term Evolution(LTE)turbo codes with only small modifications.The proposed CCSDS turbo decoder at 10 iterations on NVIDIA RTX3070 achieves about 150 Mbps and 50Mbps throughputs for the code rates 1/6 and 1/2,respectively.
基金financially supported in part by National Key R&D Program of China(No.2018YFB1801402)in part by Huawei Technologies Co.,Ltd.
文摘In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.
文摘A global optimization algorithm （GOA） for parallel Chien search circuit in Reed-Solomon （RS） （255,239） decoder is presented. By finding out the common modulo 2 additions within groups of Galois field （GF） multipliers and pre-computing the common items, the GOA can reduce the number of XOR gates efficiently and thus reduce the circuit area. Different from other local optimization algorithms, the GOA is a global one. When there are more than one maximum matches at a time, the best match choice in the GOA has the least impact on the final result by only choosing the pair with the smallest relational value instead of choosing a pair randomly. The results show that the area of parallel Chien search circuits can be reduced by 51% compared to the direct implementation when the group-based GOA is used for GF multipliers and by 26% if applying the GOA to GF multipliers separately. This optimization scheme can be widely used in general parallel architecture in which many GF multipliers are involved.
文摘The first domestic total dose hardened 2μm partially depleted silicon-on-insulator （PDSOI） CMOS 3-line to 8- line decoder fabricated in SIMOX is demonstrated. The radiation performance is characterized by transistor threshold voltage shifts,circuit static leakage currents,and I-V curves as a function of total dose up to 3× 10^5rad（Si）. The worst case threshold voltage shifts of the front channels are less than 20mV for nMOS transistors at 3 × 10^5rad（Si） and follow-up irradiation and less than 70mV for the pMOS transistors. Furthermore, no significant radiation induced leakage currents and functional degeneration are observed.
文摘A new encoder/decoder scheme of OCDMA based on waveguide is proposed in this paper. The principle as well as the structure of waveguide encoder/decoder is given. It can be seen that all optical OCDMA encoder/decoder can be realized by the proposed scheme of the waveguide encoder/decoder. It can also make the OCDMA encoder/decoder integrated easily and the access controlled easily. The system based on this scheme can work under the entirely asynchronous condition.
文摘We report the LPG pair device that can be used as a pulse duplicator or an OCDMA encoder/decoder. Due to the ring core region of dispersion compensating fiber (DCF), we can shorten the device length by a third and obtain surrounding insensitive LPG devices.
基金The National Natural Science Foundation of China(No.60871079)
文摘A modified Benes network is proposed to be used as an optimal shuffle network in worldwide interoperability for microwave access （WiMAX） low density parity check （LDPC） decoders, When the size of the input is not a power of two, the modified Benes network can achieve the most optimal performance. This modified Benes network is non-blocking and can perform any sorts of permutations, so it can support 19 modes specified in the WiMAX system. Furthermore, an efficient algorithm to generate the control signals for all the 2 × 2 switches in this network is derived, which can reduce the hardware complexity and overall latency of the modified Benes network. Synthesis results show that the proposed control signal generator can save 25.4% chip area and the overall network latency can be reduced by 36. 2%.
