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20 pages, 1843 KB  
Article
A Pipelined FPGA-Based Frame Synchronizer for Gaussian Noise Channels
by Joe Cavazos and Yuhua Chen
Electronics 2025, 14(23), 4724; https://doi.org/10.3390/electronics14234724 - 30 Nov 2025
Viewed by 257
Abstract
This paper presents a Field Programmable Gate Array (FPGA)-implementable Frame Synchronizer that overcomes deficiencies of existing synchronizers in the space communications industry and provides a pipelined approach to achieve improved performance in latency, performance in the presence of noise, and streamlined implementation complexity. [...] Read more.
This paper presents a Field Programmable Gate Array (FPGA)-implementable Frame Synchronizer that overcomes deficiencies of existing synchronizers in the space communications industry and provides a pipelined approach to achieve improved performance in latency, performance in the presence of noise, and streamlined implementation complexity. Unlike a soft decision synchronizer, magnitude (soft) bits are not required from the demodulation stage, and only the sign bit is used, reducing the complexity and signal counts between the transceiver and the synchronizer. Improved performance in noise can be achieved by introducing a small observation window surrounding the candidate Attached Sync Marker (ASM) window to uncorrelated data around the ASM. Further improvement in the presence of noise is achieved by using two ASMs, effectively doubling the ASM length of observation, but with no increase in the ASM pattern length and using existing predefined ASM patterns, thus remaining compliant with the Consultative Committee for Space Data Systems (CCSDS) standards. A parallel and pipelined implementation without a state machine eliminates latency from search, verify, lock, and flywheel states and reduces the effects of cycle slips of traditional flywheel state machine synchronizers. Full article
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37 pages, 1013 KB  
Article
Quantum–Classical Optimization for Efficient Genomic Data Transmission
by Ismael Soto, Verónica García and Pablo Palacios Játiva
Mathematics 2025, 13(17), 2792; https://doi.org/10.3390/math13172792 - 30 Aug 2025
Viewed by 916
Abstract
This paper presents a hybrid computational architecture for efficient and robust digital transmission inspired by helical genetic structures. The proposed system integrates advanced modulation schemes, such as multi-pulse-position modulation (MPPM), high-order quadrature amplitude modulation (QAM), and chirp spread spectrum (CSS), along with Reed–Solomon [...] Read more.
This paper presents a hybrid computational architecture for efficient and robust digital transmission inspired by helical genetic structures. The proposed system integrates advanced modulation schemes, such as multi-pulse-position modulation (MPPM), high-order quadrature amplitude modulation (QAM), and chirp spread spectrum (CSS), along with Reed–Solomon error correction and quantum-assisted search, to optimize performance in noisy and non-line-of-sight (NLOS) optical environments, including VLC channels modeled with log-normal fading. Through mathematical modeling and simulation, we demonstrate that the number of helical transmissions required for genome-scale data can be drastically reduced—up to 95% when using parallel strands and high-order modulation. The trade-off between redundancy, spectral efficiency, and error resilience is quantified across several configurations. Furthermore, we compare classical genetic algorithms and Grover’s quantum search algorithm, highlighting the potential of quantum computing in accelerating decision-making and data encoding. These results contribute to the field of operations research and supply chain communication by offering a scalable, energy-efficient framework for data transmission in distributed systems, such as logistics networks, smart sensing platforms, and industrial monitoring systems. The proposed architecture aligns with the goals of advanced computational modeling and optimization in engineering and operations management. Full article
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18 pages, 1149 KB  
Article
Advanced Cryptography Using Nanoantennas in Wireless Communication
by Francisco Alves, João Paulo N. Torres, P. Mendonça dos Santos and Ricardo A. Marques Lameirinhas
Information 2025, 16(9), 720; https://doi.org/10.3390/info16090720 - 22 Aug 2025
Viewed by 689
Abstract
This work presents an end-to-end encryption–decryption framework for securing electromagnetic signals processed through a nanoantenna. The system integrates amplitude normalization, uniform quantization, and Reed–Solomon forward error correction with key establishment via ECDH and bitwise XOR encryption. Two signal types were evaluated: a synthetic [...] Read more.
This work presents an end-to-end encryption–decryption framework for securing electromagnetic signals processed through a nanoantenna. The system integrates amplitude normalization, uniform quantization, and Reed–Solomon forward error correction with key establishment via ECDH and bitwise XOR encryption. Two signal types were evaluated: a synthetic Gaussian pulse and a synthetic voice waveform, representing low- and high-entropy data, respectively. For the Gaussian signal, reconstruction achieved an RMSE = 11.42, MAE = 0.86, PSNR = 26.97 dB, and Pearson’s correlation coefficient = 0.8887. The voice signal exhibited elevated error metrics, with an RMSE = 15.13, MAE = 2.52, PSNR = 24.54 dB, and Pearson correlation = 0.8062, yet maintained adequate fidelity. Entropy analysis indicated minimal changes between the original signal and the reconstructed signal. Furthermore, avalanche testing confirmed strong key sensitivity, with single-bit changes in the key altering approximately 50% of the ciphertext bits. The findings indicate that the proposed pipeline ensures high reconstruction quality with lightweight encryption, rendering it suitable for environments with limited computational resources. Full article
(This article belongs to the Section Information and Communications Technology)
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23 pages, 4254 KB  
Article
A Strongly Robust Secret Image Sharing Algorithm Based on QR Codes
by Pengcheng Huang, Canyu Chen and Xinmeng Wan
Algorithms 2025, 18(9), 535; https://doi.org/10.3390/a18090535 - 22 Aug 2025
Viewed by 1130
Abstract
Secret image sharing (SIS) is an image protection technique based on cryptography. However, traditional SIS schemes have limited noise resistance, making it difficult to ensure reconstructed image quality. To address this issue, this paper proposes a robust SIS scheme based on QR codes, [...] Read more.
Secret image sharing (SIS) is an image protection technique based on cryptography. However, traditional SIS schemes have limited noise resistance, making it difficult to ensure reconstructed image quality. To address this issue, this paper proposes a robust SIS scheme based on QR codes, which enables the efficient and lossless reconstruction of the secret image without pixel expansion. Moreover, the proposed scheme maintains high reconstruction quality under noisy conditions. In the sharing phase, the scheme compresses the length of shares by optimizing polynomial computation and improving the pixel allocation strategy. Reed–Solomon coding is then incorporated to enhance the anti-noise capability during the sharing process, while achieving meaningful secret sharing using QR codes as carriers. In the reconstruction phase, the scheme further improves the quality of the reconstructed secret image by combining image inpainting algorithms with the error-correction capability of Reed–Solomon codes. The experimental results show that the scheme can achieve lossless reconstruction when the salt-and-pepper noise density is less than d0.02, and still maintains high-quality reconstruction when d0.13. Compared with the existing schemes, the proposed method significantly improves noise robustness without pixel expansion, while preserving the visual meaning of the QR code carrier, and achieves a secret sharing strategy that combines robustness and practicality. Full article
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16 pages, 1863 KB  
Article
Improving Data Communication of Enhanced Loran Systems Using 128-ary Polar Codes
by Ruochen Jia, Yunxiao Li and Daiming Qu
Sensors 2025, 25(15), 4638; https://doi.org/10.3390/s25154638 - 26 Jul 2025
Viewed by 1362
Abstract
The enhanced Loran (eLoran) system, a critical terrestrial backup for the Global Satellite Navigation System (GNSS), traditionally utilizes a Reed-Solomon (RS) code for its data communication, which presents limitations in error performance, particularly due to its decoding method. This paper introduces a significant [...] Read more.
The enhanced Loran (eLoran) system, a critical terrestrial backup for the Global Satellite Navigation System (GNSS), traditionally utilizes a Reed-Solomon (RS) code for its data communication, which presents limitations in error performance, particularly due to its decoding method. This paper introduces a significant advancement by proposing the replacement of the conventional RS code with a 128-ary polar code, which is designed to maintain compatibility with the established 128-ary Pulse Position Modulation (PPM) scheme integral to eLoran’s positioning function. A Soft–Soft (SS) demodulation method, based on a correlation receiver, is developed to provide the requisite soft information for the effective Successive Cancellation List (SCL) decoding of the 128-ary polar code. Comprehensive simulations demonstrate that the proposed 128-ary polar code with SS demodulation achieves a substantial error performance improvement, yielding an approximate 9.3 dB gain at the 0.01 FER level over the RS code in eLoran data communication with EPD-MD demodulation. Additionally, the proposed scheme improves data transmission efficiency—either reducing transmission duration by 2/3 or increasing message bit number by 250% for comparable error performance—without impacting the system’s primary positioning capabilities. Full article
(This article belongs to the Section Communications)
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16 pages, 3971 KB  
Article
Enhancing Radiation Resilience and Throughput in Spaceborne RS(255,223) Encoder via Interleaved Pipelined Architecture
by Xufeng Li, Li Zhou and Yan Zhu
Electronics 2025, 14(12), 2447; https://doi.org/10.3390/electronics14122447 - 16 Jun 2025
Viewed by 620
Abstract
The error correction capability of the RS(255,223) code has been significantly enhanced compared to that of the RS(256,252) code, making it the preferred choice for the next generation of onboard solid-state recorders (O-SSRs). With the application of non-volatile double data rate (NV-DDR) interface [...] Read more.
The error correction capability of the RS(255,223) code has been significantly enhanced compared to that of the RS(256,252) code, making it the preferred choice for the next generation of onboard solid-state recorders (O-SSRs). With the application of non-volatile double data rate (NV-DDR) interface technology in O-SSRs, instantaneous transmission rates of up to 1 Gbps per data I/O interface can be achieved. This development imposes higher requirements on the encoding throughput of RS encoders. For RS(255,223) encoders, throughput improvement is limited by the structures of serial architectures. The algorithm’s inherent characteristics restrict the depth of pipelining. In contrast, parallel solutions face bottlenecks in resource efficiency. To address these challenges, an interleaved pipelined architecture is proposed. By integrating interleaving technology within the pipeline, the structure overcomes the limitations of serial architectures. Using this architecture, a 36-stage pipelined RS(255,223) encoder is implemented. The throughput is greatly enhanced, and the radiation tolerance is also improved due to the application of interleaving techniques. The RS(255,223) encoder performance was evaluated on the Xilinx XC7K325T platform. The results confirm that the proposed architecture can support high data rates and provide effective error correction. With an 8-bit symbol size, a single encoder achieved throughput of 3.043 Gbps, making it highly suitable for deployment in future space exploration missions. Full article
(This article belongs to the Special Issue Emerging Applications of FPGAs and Reconfigurable Computing System)
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17 pages, 1021 KB  
Article
Compressive Sensing-Based Coding Iterative Channel Estimation Method for TDS-OFDM System
by Yuxiao Yang, Xinyue Zhao and Hui Wang
Electronics 2025, 14(12), 2338; https://doi.org/10.3390/electronics14122338 - 7 Jun 2025
Viewed by 774
Abstract
Satellite Internet is the key to integrated air–space–ground communication, while the design of waveforms with high spectrum efficiency is an intrinsic requirement for high-speed data transmission in satellite Internet. Time-domain synchronous orthogonal frequency division multiplexing (TDS-OFDM) technology can significantly improve spectrum utilization efficiency [...] Read more.
Satellite Internet is the key to integrated air–space–ground communication, while the design of waveforms with high spectrum efficiency is an intrinsic requirement for high-speed data transmission in satellite Internet. Time-domain synchronous orthogonal frequency division multiplexing (TDS-OFDM) technology can significantly improve spectrum utilization efficiency by using PN sequences instead of traditional CP cyclic prefixes. However, it also leads to time-domain aliasing between PN sequences and data symbols, posing a serious challenge to channel estimation. To solve this problem, a compressive sensing-based coding iterative channel estimation method for the TDS-OFDM system is proposed in this paper. This method innovatively combines compressive sensing channel estimation technology with the Reed–Solomon low-density parity-check cascade coding (RS-LDPC) scheme, and achieves performance improvements as follows: (1) Construct the iterative optimization mechanism for the compressive sensing algorithm and equalization feedback loop. (2) RS-LDPC cascaded coding is employed to enhance the anti-interference and error correction capability of system. (3) Design the recoding link of error-corrected data to improve the accuracy of sensing matrix. The simulation results demonstrate that compared with conventional methods, the proposed method can obviously converge on the mean squared errors (MSEs) of channel estimation and significantly reduce the bit error rate (BER) of the system. Full article
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18 pages, 5158 KB  
Article
Research on Maximum Likelihood Decoding Algorithm and Channel Characteristics Optimization for 4FSK Ultraviolet Communication System Based on Poisson Distribution
by Li Kuang, Yingkai Zhao, Kangjian Li, Xingfa Wang, Linyi Li, Huishi Zhu, Weijie Zhang and Jianguo Liu
Photonics 2025, 12(5), 419; https://doi.org/10.3390/photonics12050419 - 27 Apr 2025
Viewed by 717
Abstract
This study focuses on a 4FSK-modulated ultraviolet (UV) communication system, introducing an innovative symbol-level maximum likelihood decoding approach based on Poisson statistics. A forward error correction (FEC) coding mechanism is integrated to enhance system robustness. Through Monte Carlo simulations, the proposed decoding scheme [...] Read more.
This study focuses on a 4FSK-modulated ultraviolet (UV) communication system, introducing an innovative symbol-level maximum likelihood decoding approach based on Poisson statistics. A forward error correction (FEC) coding mechanism is integrated to enhance system robustness. Through Monte Carlo simulations, the proposed decoding scheme and the error correction performances of Reed–Solomon (RS) and Low-Density Parity-Check (LDPC) codes are evaluated in UV channels. Both RS and LDPC codes significantly improve the Bit Error Rate (BER), with LDPC codes achieving superior gains under low SNR conditions. Hardware implementation and field tests validate the decoding algorithm and LDPC-optimized 4FSK system. Under non-line-of-sight (NLOS) conditions (10–45° transmit elevation angle), stable 60 m communication with BER < 10−3 is achieved. In line-of-sight (LOS) scenarios, the system demonstrates 900 m range with BER < 10−3, highlighting practical applicability in challenging atmospheric environments. Full article
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11 pages, 3601 KB  
Article
Image Storage in DNA by an Extensible Quaternary Codec System
by Ruoying Pang, Yiming Dong and Xin Zhao
Appl. Sci. 2025, 15(9), 4760; https://doi.org/10.3390/app15094760 - 25 Apr 2025
Viewed by 1384
Abstract
Silicon-based storage technologies are increasingly failing to meet the explosively growing data storage demands of the information age. DNA-based data storage offers a promising solution due to its unparalleled storage density, long lifespan, low energy consumption, and high parallel accessibility. In this study, [...] Read more.
Silicon-based storage technologies are increasingly failing to meet the explosively growing data storage demands of the information age. DNA-based data storage offers a promising solution due to its unparalleled storage density, long lifespan, low energy consumption, and high parallel accessibility. In this study, we propose a novel True Quadratic Codec System (ETQ) that directly encodes data into nucleotide sequences using a quaternary encoding approach. By treating A, T, C, and G as direct encoding symbols (0, 1, 2, 3), an ETQ eliminates the intermediate binary-to-ATCG conversion step, thus surpassing the theoretical storage density limit of 2 bits/nt. An ETQ is built on these three key components: (1) dividing image data into B, G, and R color channels for separate encoding and storage, (2) employing quaternary Huffman encoding to map image information directly into nucleotide sequences, and (3) integrating Reed–Solomon error correction codes to enhance data reliability and system extensibility. The ETQ framework demonstrates significant improvements in storage density and efficiency compared to conventional methods. By leveraging the inherent properties of DNA, this system offers a scalable and cost-effective solution that addresses the growing global data storage crisis. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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14 pages, 1376 KB  
Article
Ultra-Wideband Analog Radio-over-Fiber Communication System Employing Pulse-Position Modulation
by Sandis Migla, Kristaps Rubuls, Nikolajs Tihomorskis, Toms Salgals, Oskars Ozolins, Vjaceslavs Bobrovs, Sandis Spolitis and Arturs Aboltins
Appl. Sci. 2025, 15(8), 4222; https://doi.org/10.3390/app15084222 - 11 Apr 2025
Cited by 1 | Viewed by 1665
Abstract
This research presents a novel approach to 28 GHz impulse radio ultra-wideband (IR-UWB) transmission using pulse position modulation (PPM) over an analog radio-over-fiber (ARoF) link, investigating the impact of fiber-based fronthaul on the overall performance of the communication system. In this setup, an [...] Read more.
This research presents a novel approach to 28 GHz impulse radio ultra-wideband (IR-UWB) transmission using pulse position modulation (PPM) over an analog radio-over-fiber (ARoF) link, investigating the impact of fiber-based fronthaul on the overall performance of the communication system. In this setup, an arbitrary waveform generator (AWG) is employed for PPM signal generation, while demodulation is performed with a commercial time-to-digital converter (TDC) based on an event timer. To enhance the reliability of transmitted reference PPM (TR-PPM) signals, the transmission system integrates Gray coding and Consultative Committee for Space Data Systems (CCSDS)-standard-compliant Reed-Solomon (RS) error correcting code (ECC). System performance was evaluated by transmitting pseudorandom binary sequences (PRBSs) and measuring the bit error ratio (BER) across a 5-m wireless link between two 20 dBi gain horn (Ka-band) antennas, with and without a 20 km single-mode optical fiber (SMF) link in transmitter side and ECC at the receiver side. The system achieved a BER of less than 8.17 × 10−7, using a time bin duration of 200 ps and a pulse duration of 100 ps, demonstrating robust performance and significant potential for space-to-ground telecommunication applications. Full article
(This article belongs to the Special Issue Recent Advances in Microwave Devices and Intelligent Systems)
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21 pages, 8764 KB  
Article
Design and Implementation of a High-Reliability Underwater Wireless Optical Communication System Based on FPGA
by Tengfei Han, Peng Ding, Nan Liu, Zhengguang Wang, Zhenyao Li, Zhanqiang Ru, Helun Song and Zhizhen Yin
Appl. Sci. 2025, 15(7), 3544; https://doi.org/10.3390/app15073544 - 24 Mar 2025
Cited by 4 | Viewed by 2067
Abstract
In order to meet the reliability requirements of communication for underwater resource exploration, this study develops an underwater wireless optical communication (UWOC) system utilizing a blue semiconductor laser as the light source. At the receiver, a fully digital automatic gain control (AGC) module, [...] Read more.
In order to meet the reliability requirements of communication for underwater resource exploration, this study develops an underwater wireless optical communication (UWOC) system utilizing a blue semiconductor laser as the light source. At the receiver, a fully digital automatic gain control (AGC) module, implemented on a field-programmable gate array (FPGA), is designed to mitigate signal fluctuations induced by underwater turbulence. Digital filtering techniques, including median filtering (MF) and bilateral edge detection filtering (BEDF), are also employed to improve signal demodulation reliability. An improved Reed–Solomon (RS) coding scheme is further adopted to significantly reduce the bit error rate (BER). The design of a highly reliable UWOC system was realized based on the above techniques. The system’s performance was evaluated across a range of signal-to-noise ratios (SNRs) and bubble intensities. The results show that the digital AGC module can provide a gain range from −3.2 dB to 16 dB, adapting to varying signal strengths, which greatly bolsters the system’s resilience against underwater turbulence. Filtering techniques and RS coding further enhance the system’s immunity to interference and reduce the system BER. Communication experiments were conducted over various distances under three distinct water quality conditions. The results demonstrate that, within the detection range of the avalanche photodiode (APD), the system consistently maintained a BER below 3.8 × 10−3 across all water types, thereby confirming its high reliability. In clear seawater, the system demonstrated reliable information transmission over a 10 m distance at a data rate of 10 Mbps, achieving a BER of 2 × 10−8. Theoretical calculations indicate that the maximum transmission distance in clear seawater can reach 111.35 m. Full article
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14 pages, 4634 KB  
Article
High-Reliability Wireless Pressure Measurement System Based on FEC Algorithm
by Shangwen Gong, Zhengyan Wang and Huixin Zhang
Electronics 2025, 14(6), 1196; https://doi.org/10.3390/electronics14061196 - 18 Mar 2025
Viewed by 539
Abstract
As the core of an aircraft’s power system, the stability and reliability of an aero-engine’s performance are crucial to flight safety. Addressing the issues of complex wiring and poor flexibility in traditional wired testing systems, this paper designs and implements a wireless transmission [...] Read more.
As the core of an aircraft’s power system, the stability and reliability of an aero-engine’s performance are crucial to flight safety. Addressing the issues of complex wiring and poor flexibility in traditional wired testing systems, this paper designs and implements a wireless transmission aero-engine pressure measurement system based on FPGA. By integrating front-end memory and a back-end test bench and utilizing LoRa wireless communication technology and the Reed–Solomon (RS) forward error correction (FEC) algorithm, the system significantly enhances the reliability and anti-interference capability of data transmission. Test results demonstrate that the system can monitor and record engine pressure parameters in real time in complex environments, with a notable reduction in bit error rate and packet loss rate, especially under strong interference conditions. This system resolves wiring challenges, enhances the real-time performance of monitoring links and the stability of data storage, and is characterized by high precision, high reliability, and automation. It is suitable for complex and harsh working environments and has broad application prospects in the aviation and military sectors. Full article
(This article belongs to the Special Issue Digital Signal Processing and Wireless Communication)
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22 pages, 2728 KB  
Article
Hybrid Dynamic Galois Field with Quantum Resilience for Secure IoT Data Management and Transmission in Smart Cities Using Reed–Solomon (RS) Code
by Abdullah Aljuhni, Amer Aljaedi, Adel R. Alharbi, Ahmed Mubaraki and Moahd K. Alghuson
Symmetry 2025, 17(2), 259; https://doi.org/10.3390/sym17020259 - 8 Feb 2025
Cited by 2 | Viewed by 1506
Abstract
The Internet of Things (IoT), which is characteristic of the current industrial revolutions, is the connection of physical devices through different protocols and sensors to share information. Even though the IoT provides revolutionary opportunities, its connection to the current Internet for smart cities [...] Read more.
The Internet of Things (IoT), which is characteristic of the current industrial revolutions, is the connection of physical devices through different protocols and sensors to share information. Even though the IoT provides revolutionary opportunities, its connection to the current Internet for smart cities brings new opportunities for security threats, especially with the appearance of new threats like quantum computing. Current approaches to protect IoT data are not immune to quantum attacks and are not designed to offer the best data management for smart city applications. Thus, post-quantum cryptography (PQC), which is still in its research stage, aims to solve these problems. To this end, this research introduces the Dynamic Galois Reed–Solomon with Quantum Resilience (DGRS-QR) system to improve the secure management and communication of data in IoT smart cities. The data preprocessing includes K-Nearest Neighbors (KNN) and min–max normalization and then applying the Galois Field Adaptive Expansion (GFAE). Optimization of the quantum-resistant keys is accomplished by applying Artificial Bee Colony (ABC) and Moth Flame Optimization (MFO) algorithms. Also, role-based access control provides strong cloud data security, and quantum resistance is maintained by refreshing keys every five minutes of the active session. For error correction, Reed–Solomon (RS) codes are used which provide data reliability. Data management is performed using an attention-based Bidirectional Long Short-Term Memory (Att-Bi-LSTM) model with skip connections to provide optimized city management. The proposed approach was evaluated using key performance metrics: a key generation time of 2.34 s, encryption time of 4.56 s, decryption time of 3.56 s, PSNR of 33 dB, and SSIM of 0.99. The results show that the proposed system is capable of protecting IoT data from quantum threats while also ensuring optimal data management and processing. Full article
(This article belongs to the Special Issue New Advances in Symmetric Cryptography)
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16 pages, 2495 KB  
Article
A Novel Architecture for Addressing the Throughput Bottleneck in Spaceborne Solid-State Recorder for Electromagnetic Spectrum Sensors
by Xufeng Li, Li Zhou and Yan Zhu
Remote Sens. 2025, 17(1), 138; https://doi.org/10.3390/rs17010138 - 3 Jan 2025
Cited by 1 | Viewed by 1170
Abstract
The data acquisition rate of electromagnetic spectrum sensors is exceedingly high. However, the throughput of current high-speed spaceborne solid-state recorders (S-SSR) remains relatively low, making it difficult for the data to be fully stored. To address this issue, a novel architecture for a [...] Read more.
The data acquisition rate of electromagnetic spectrum sensors is exceedingly high. However, the throughput of current high-speed spaceborne solid-state recorders (S-SSR) remains relatively low, making it difficult for the data to be fully stored. To address this issue, a novel architecture for a high-speed S-SSR is introduced in this study. The throughput of the S-SSR is primarily limited by three factors: the performance of the error-checking algorithm, the inability of a single FPGA to support the parallel expansion of too many Flash chips due to its limited effective I/O pins, and the efficiency of FLASH control. In the proposed architecture, a 10-stage pipelined RS(252,256) code is implemented. Data are distributed and stored in different memory regions controlled by separate FPGAs. Interleaved storage, multi-plane, and cache operation FLASH control module are also employed to resolve these bottlenecks. To further increase the throughput of the S-SSR, the system clock distribution has been optimized. In addition, interleaved encoding technology has been applied to improve radiation resistance and ensure data integrity. The performance of the system was evaluated on the Xilinx XC7K325T platform. The results confirm that the architecture is capable of handling high data rates and effectively correcting errors. The system can achieve a throughput of 46.8948 Gbps, making it suitable for future deployment in space exploration missions. Full article
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12 pages, 332 KB  
Article
On Matrix Representation of Extension Field GF(pL) and Its Application in Vector Linear Network Coding
by Hanqi Tang, Heping Liu, Sheng Jin, Wenli Liu and Qifu Sun
Entropy 2024, 26(10), 822; https://doi.org/10.3390/e26100822 - 26 Sep 2024
Cited by 1 | Viewed by 1202
Abstract
For a finite field GF(pL) with prime p and L>1, one of the standard representations is L×L matrices over GF(p) so that the arithmetic of GF(pL) can be realized by [...] Read more.
For a finite field GF(pL) with prime p and L>1, one of the standard representations is L×L matrices over GF(p) so that the arithmetic of GF(pL) can be realized by the arithmetic among these matrices over GF(p). Based on the matrix representation of GF(pL), a conventional linear network coding scheme over GF(pL) can be transformed to an L-dimensional vector LNC scheme over GF(p). Recently, a few real implementations of coding schemes over GF(2L), such as the Reed–Solomon (RS) codes in the ISA-L library and the Cauchy-RS codes in the Longhair library, are built upon the classical result to achieve matrix representation, which focuses more on the structure of every individual matrix but does not shed light on the inherent correlation among matrices which corresponds to different elements. In this paper, we first generalize this classical result from over GF(2L) to over GF(pL) and paraphrase it from the perspective of matrices with different powers to make the inherent correlation among these matrices more transparent. Moreover, motivated by this correlation, we can devise a lookup table to pre-store the matrix representation with a smaller size than the one utilized in current implementations. In addition, this correlation also implies useful theoretical results which can be adopted to further demonstrate the advantages of binary matrix representation in vector LNC. In the following part of this paper, we focus on the study of vector LNC and investigate the applications of matrix representation related to the aspects of random and deterministic vector LNC. Full article
(This article belongs to the Special Issue Information Theory and Network Coding II)
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