Implementing check node(CN)update based on the minimum value(MV)and second MV of incoming message magnitudes is crucial for Min-Sum Algorithms(MSAs).In the category of bit-serial implementations,existing schemes suffe...Implementing check node(CN)update based on the minimum value(MV)and second MV of incoming message magnitudes is crucial for Min-Sum Algorithms(MSAs).In the category of bit-serial implementations,existing schemes suffer from decoding performance degradation,large hardware areas,and/or long latency.In this paper,we propose two efficient CN update functions based on the MV and an approximate second MV,and design bit-serial architectures to implement them.Simulation results show that our functions exhibit the minimum decoding performance degradation compared to the existing functions using approximate second MVs.Moreover,the applicationspecific integrated circuits(ASIC)implementation results demonstrate the advantages of our architectures in terms of area,latency,etc.展开更多
Aiming at the poor performance of the parity check(PC) aided adaptive successive cancellation list(PC-ASCL) decoding algorithm because the PC code in the polar code can only verify odd errors, an optimized parity chec...Aiming at the poor performance of the parity check(PC) aided adaptive successive cancellation list(PC-ASCL) decoding algorithm because the PC code in the polar code can only verify odd errors, an optimized parity check(OPC) code which can verify all odd errors as well as the half even errors is proposed. The OPC code is used to improve the PC-ASCL decoding algorithm, thus an OPC aided ASCL(OPC-ASCL) decoding algorithm is proposed. In the coding stage, the algorithm divides the information sequence into multiple segments, and places an OPC code at the end of each segment to verify the current information sequence, and places a cyclic redundancy check code at the end of the entire information sequence to verify the entire information sequence. In the decoding stage, the algorithm uses the OPC-ASCL decoder to decode. Simulation results show that compared to the PC-ASCL decoding algorithm, the OPC-ASCL decoding algorithm can reduce the complexity and obtain the certain performance gain.展开更多
Space laser communication(SLC)is an emerging technology to support high-throughput data transmissions in space networks.In this paper,to guarantee the reliability of high-speed SLC links,we aim at practical implementa...Space laser communication(SLC)is an emerging technology to support high-throughput data transmissions in space networks.In this paper,to guarantee the reliability of high-speed SLC links,we aim at practical implementation of low-density paritycheck(LDPC)decoding under resource-restricted space platforms.Particularly,due to the supply restriction and cost issues of high-speed on-board devices such as analog-to-digital converters(ADCs),the input of LDPC decoding will be usually constrained by hard-decision channel output.To tackle this challenge,density-evolution-based theoretical analysis is firstly performed to identify the cause of performance degradation in the conventional binaryinitialized iterative decoding(BIID)algorithm.Then,a computation-efficient decoding algorithm named multiary-initialized iterative decoding with early termination(MIID-ET)is proposed,which improves the error-correcting performance and computation efficiency by using a reliability-based initialization method and a threshold-based decoding termination rule.Finally,numerical simulations are conducted on example codes of rates 7/8 and 1/2 to evaluate the performance of different LDPC decoding algorithms,where the proposed MIID-ET outperforms the BIID with a coding gain of 0.38 dB and variable node calculation saving of 37%.With this advantage,the proposed MIID-ET can notably reduce LDPC decoder’s hardware implementation complexity under the same bit error rate performance,which successfully doubles the total throughput to 10 Gbps on a single-chip FPGA.展开更多
针对可见光信道中的干扰较强,且现阶段OCC(Optical Camera Communication)系统的编码技术纠错性能不足,造成OCC系统可靠性降低的问题,提出了一种面向OCC系统的QC-LDPC(Quasi-Cyclic Low Density Parity Check Code)编译码算法。根据OCC...针对可见光信道中的干扰较强,且现阶段OCC(Optical Camera Communication)系统的编码技术纠错性能不足,造成OCC系统可靠性降低的问题,提出了一种面向OCC系统的QC-LDPC(Quasi-Cyclic Low Density Parity Check Code)编译码算法。根据OCC系统的结构特点以及信道链路特性,确定具有结构化设计和低复杂度译码特性的QC-LDPC码作为纠错码型,采用快速编码算法减小编码过程的运算复杂度;结合归一化最小和算法和分层译码算法的各自特点提出了一种改进的L-MS(Layer-Min Sum)译码算法。OCC系统实验平台测试结果表明,在室内环境通信场景下,OCC系统的误码率为3.16×10-6,通信速率为2850.4 bit/s;在室外环境通信场景下,OCC系统的误码率为9.07×10-6,通信速率为2797.9 bit/s,在保证低误码率的同时,兼顾了数据的传输速率。展开更多
Abstract: The layered decoding algorithm has been widely used in the implementation of Low Density Parity Check (LDPC) decoders, due to its high convergence speed. However, the pipeline operation of the layered dec...Abstract: The layered decoding algorithm has been widely used in the implementation of Low Density Parity Check (LDPC) decoders, due to its high convergence speed. However, the pipeline operation of the layered decoder may introduce memory access conflicts, which heavily deteriorates the decoder throughput. To essentially deal with the issue of memory access conflicts,展开更多
A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbo...A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbol vector iteratively in search of a valid codeword in the symbol vector space. Only one symbol is flipped in each iteration, and symbol flipping function, which is employed as the symbol flipping metric, combines the number of failed checks and the reliabilities of the received bits and calculated symbols. A scheme to avoid infinite loops and select one symbol to flip in high order Galois field search is also proposed. The design of flipping pattern's order and depth, which is dependent of the computational requirement and error performance, is also proposed and exemplified. Simulation results show that the algorithm achieves an appealing tradeoff between performance and computational requirement over relatively low Galois field for short to medium code length.展开更多
This paper presents a simple yet effective decoding for general quasi-cyclic low-density parity-check (QC-LDPC) codes, which not only achieves high hardware utility efficiency (HUE), but also brings about great me...This paper presents a simple yet effective decoding for general quasi-cyclic low-density parity-check (QC-LDPC) codes, which not only achieves high hardware utility efficiency (HUE), but also brings about great memory block reduction without any performance degradation. The main idea is to split the check matrix into several row blocks, then to perform the improved mes- sage passing computations sequentially block by block. As the decoding algorithm improves, the sequential tie between the two-phase computations is broken, so that the two-phase computations can be overlapped which bring in high HUE. Two over- lapping schemes are also presented, each of which suits a different situation. In addition, an efficient memory arrangement scheme is proposed to reduce the great memory block requirement of the LDPC decoder. As an example, for the 0.4 rate LDPC code selected from Chinese Digital TV Terrestrial Broadcasting (DTTB), our decoding saves over 80% memory blocks com- pared with the conventional decoding, and the decoder achieves 0.97 HUE. Finally, the 0.4 rate LDPC decoder is implemented on an FPGA device EP2S30 (speed grade -5). Using 8 row processing units, the decoder can achieve a maximum net throughput of 28.5 Mbps at 20 iterations.展开更多
Non-uniform quantization for messages in Low-Density Parity-Check(LDPC)decoding canreduce implementation complexity and mitigate performance loss.But the distribution of messagesvaries in the iterative decoding.This l...Non-uniform quantization for messages in Low-Density Parity-Check(LDPC)decoding canreduce implementation complexity and mitigate performance loss.But the distribution of messagesvaries in the iterative decoding.This letter proposes a variable non-uniform quantized Belief Propaga-tion(BP)algorithm.The BP decoding is analyzed by density evolution with Gaussian approximation.Since the probability density of messages can be well approximated by Gaussian distribution,by theunbiased estimation of variance,the distribution of messages can be tracked during the iteration.Thusthe non-uniform quantization scheme can be optimized to minimize the distortion.Simulation resultsshow that the variable non-uniform quantization scheme can achieve better error rate performance andfaster decoding convergence than the conventional non-uniform quantization and uniform quantizationschemes.展开更多
A network-coding-based multisource LDPC-coded cooperative MIMO scheme is proposed,where multiple sources transmit their messages to the destination with the assistance from a single relay.The relay cooperates with mul...A network-coding-based multisource LDPC-coded cooperative MIMO scheme is proposed,where multiple sources transmit their messages to the destination with the assistance from a single relay.The relay cooperates with multiple sources simultaneously via network-coding.It avoids the issues of imperfect frequencyiming synchronization and large transmission delay which may be introduced by frequency-division multiple access(FDMA)/code-division multiple access(CDMA)and time-division multiple access(TDMA)manners.The proposed joint″Min-Sum″iterative decoding is effectively carried out in the destination.Such a decoding algorithm agrees with the introduced equivalent joint Tanner graph which can be used to fully characterize LDPC codes employed by the sources and relay.Theoretical analysis and numerical simulation show that the proposed scheme with joint iterative decoding can achieve significant cooperation diversity gain.Furthermore,for the relay,compared with the cascade scheme,the proposed scheme has much lower complexity of LDPC-encoding and is easier to be implemented in the hardware with similar bit error rate(BER)performance.展开更多
In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are de...In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are derived by permuting the matrices of the corresponding RC-LDPC block codes,are systematic and have maximum encoding memory.Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation(BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels(BI-AWGNCs).展开更多
Two modified BP algorithms related to vertical and horizontal processes are proposed to accelerate iterative low-density parity- check (LDPC) decoding over an additive white Gaussian noise (AWGN) channel, where th...Two modified BP algorithms related to vertical and horizontal processes are proposed to accelerate iterative low-density parity- check (LDPC) decoding over an additive white Gaussian noise (AWGN) channel, where the newly updated extrinsic information is immediately used in the current decoding round. Theoretical analysis and simulation results demonstrate that both the modified approaches provide significant performance improvements over the traditional BP algorithm with almost no additional decoding complexity. The proposed algorithm with modified horizontal process offers even better performance than another algorithm with the modified horizontal process. The two modified BP algorithms are very promising in practical communications since both can achieve an excellent trade-off between the performance and decoding complexity.展开更多
In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destinatio...In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destination which is in accordance with the corresponding joint Tanner graph characterizing two different component LDPC codes used by the source and relay in ideal and non-ideal relay cooperations. The theoretical analysis and simulations show that the coded cooperation scheme obviously outperforms the coded non-cooperation one under the same code rate and decoding complex. The significant performance improvement can be virtually credited to the additional mutual exchange of the extrinsic information resulted by the LDPC code employed by the source and its counterpart used by the relay in both ideal and non-ideal cooperations.展开更多
As an effective error correction technology,the Low Density Parity Check Code(LDPC)has been researched and applied by many scholars.Meanwhile,LDPC codes have some prominent performances,which involves close to the Sha...As an effective error correction technology,the Low Density Parity Check Code(LDPC)has been researched and applied by many scholars.Meanwhile,LDPC codes have some prominent performances,which involves close to the Shannon limit,achieving a higher bit rate and a fast decoding.However,whether these excellent characteristics are suitable for the resource-constrained Wireless Sensor Network(WSN),it seems to be seldom concerned.In this article,we review the LDPC code’s structure brief.ly,and them classify and summarize the LDPC codes’construction and decoding algorithms,finally,analyze the applications of LDPC code for WSN.We believe that our contributions will be able to facilitate the application of LDPC code in WSN.展开更多
基金supported by National Natural Science Foundation of China(NSFC)under Grant 62571455,Grant 62371401,and Grant 62331002supported by the SingaporeMinistry of Education Academic Research Fund Tier 2 T2EP50221-0036.
摘要Implementing check node(CN)update based on the minimum value(MV)and second MV of incoming message magnitudes is crucial for Min-Sum Algorithms(MSAs).In the category of bit-serial implementations,existing schemes suffer from decoding performance degradation,large hardware areas,and/or long latency.In this paper,we propose two efficient CN update functions based on the MV and an approximate second MV,and design bit-serial architectures to implement them.Simulation results show that our functions exhibit the minimum decoding performance degradation compared to the existing functions using approximate second MVs.Moreover,the applicationspecific integrated circuits(ASIC)implementation results demonstrate the advantages of our architectures in terms of area,latency,etc.
基金supported by the National Natural Science Foundation of China(Nos.U21A20447 and 61971079)。
摘要Aiming at the poor performance of the parity check(PC) aided adaptive successive cancellation list(PC-ASCL) decoding algorithm because the PC code in the polar code can only verify odd errors, an optimized parity check(OPC) code which can verify all odd errors as well as the half even errors is proposed. The OPC code is used to improve the PC-ASCL decoding algorithm, thus an OPC aided ASCL(OPC-ASCL) decoding algorithm is proposed. In the coding stage, the algorithm divides the information sequence into multiple segments, and places an OPC code at the end of each segment to verify the current information sequence, and places a cyclic redundancy check code at the end of the entire information sequence to verify the entire information sequence. In the decoding stage, the algorithm uses the OPC-ASCL decoder to decode. Simulation results show that compared to the PC-ASCL decoding algorithm, the OPC-ASCL decoding algorithm can reduce the complexity and obtain the certain performance gain.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1005000)the National Natural Science Foundation of China(Grant No.62101308 and 62025110).
摘要Space laser communication(SLC)is an emerging technology to support high-throughput data transmissions in space networks.In this paper,to guarantee the reliability of high-speed SLC links,we aim at practical implementation of low-density paritycheck(LDPC)decoding under resource-restricted space platforms.Particularly,due to the supply restriction and cost issues of high-speed on-board devices such as analog-to-digital converters(ADCs),the input of LDPC decoding will be usually constrained by hard-decision channel output.To tackle this challenge,density-evolution-based theoretical analysis is firstly performed to identify the cause of performance degradation in the conventional binaryinitialized iterative decoding(BIID)algorithm.Then,a computation-efficient decoding algorithm named multiary-initialized iterative decoding with early termination(MIID-ET)is proposed,which improves the error-correcting performance and computation efficiency by using a reliability-based initialization method and a threshold-based decoding termination rule.Finally,numerical simulations are conducted on example codes of rates 7/8 and 1/2 to evaluate the performance of different LDPC decoding algorithms,where the proposed MIID-ET outperforms the BIID with a coding gain of 0.38 dB and variable node calculation saving of 37%.With this advantage,the proposed MIID-ET can notably reduce LDPC decoder’s hardware implementation complexity under the same bit error rate performance,which successfully doubles the total throughput to 10 Gbps on a single-chip FPGA.
基金the National Natural Science Foundation of China,the National Key Basic Research Program of China,The authors would like to thank all project partners for their valuable contributions and feedbacks
摘要Abstract: The layered decoding algorithm has been widely used in the implementation of Low Density Parity Check (LDPC) decoders, due to its high convergence speed. However, the pipeline operation of the layered decoder may introduce memory access conflicts, which heavily deteriorates the decoder throughput. To essentially deal with the issue of memory access conflicts,
摘要A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbol vector iteratively in search of a valid codeword in the symbol vector space. Only one symbol is flipped in each iteration, and symbol flipping function, which is employed as the symbol flipping metric, combines the number of failed checks and the reliabilities of the received bits and calculated symbols. A scheme to avoid infinite loops and select one symbol to flip in high order Galois field search is also proposed. The design of flipping pattern's order and depth, which is dependent of the computational requirement and error performance, is also proposed and exemplified. Simulation results show that the algorithm achieves an appealing tradeoff between performance and computational requirement over relatively low Galois field for short to medium code length.
基金Science and Technology on Avionics Integration Laboratory and Aeronautical Science Foundation of China (20115551022)
摘要This paper presents a simple yet effective decoding for general quasi-cyclic low-density parity-check (QC-LDPC) codes, which not only achieves high hardware utility efficiency (HUE), but also brings about great memory block reduction without any performance degradation. The main idea is to split the check matrix into several row blocks, then to perform the improved mes- sage passing computations sequentially block by block. As the decoding algorithm improves, the sequential tie between the two-phase computations is broken, so that the two-phase computations can be overlapped which bring in high HUE. Two over- lapping schemes are also presented, each of which suits a different situation. In addition, an efficient memory arrangement scheme is proposed to reduce the great memory block requirement of the LDPC decoder. As an example, for the 0.4 rate LDPC code selected from Chinese Digital TV Terrestrial Broadcasting (DTTB), our decoding saves over 80% memory blocks com- pared with the conventional decoding, and the decoder achieves 0.97 HUE. Finally, the 0.4 rate LDPC decoder is implemented on an FPGA device EP2S30 (speed grade -5). Using 8 row processing units, the decoder can achieve a maximum net throughput of 28.5 Mbps at 20 iterations.
基金the Aerospace Technology Support Foun-dation of China(No.J04-2005040).
摘要Non-uniform quantization for messages in Low-Density Parity-Check(LDPC)decoding canreduce implementation complexity and mitigate performance loss.But the distribution of messagesvaries in the iterative decoding.This letter proposes a variable non-uniform quantized Belief Propaga-tion(BP)algorithm.The BP decoding is analyzed by density evolution with Gaussian approximation.Since the probability density of messages can be well approximated by Gaussian distribution,by theunbiased estimation of variance,the distribution of messages can be tracked during the iteration.Thusthe non-uniform quantization scheme can be optimized to minimize the distortion.Simulation resultsshow that the variable non-uniform quantization scheme can achieve better error rate performance andfaster decoding convergence than the conventional non-uniform quantization and uniform quantizationschemes.
基金Supported by the Postdoctoral Science Foundation of China(2014M561694)the Science and Technology on Avionics Integration Laboratory and National Aeronautical Science Foundation of China(20105552)
摘要A network-coding-based multisource LDPC-coded cooperative MIMO scheme is proposed,where multiple sources transmit their messages to the destination with the assistance from a single relay.The relay cooperates with multiple sources simultaneously via network-coding.It avoids the issues of imperfect frequencyiming synchronization and large transmission delay which may be introduced by frequency-division multiple access(FDMA)/code-division multiple access(CDMA)and time-division multiple access(TDMA)manners.The proposed joint″Min-Sum″iterative decoding is effectively carried out in the destination.Such a decoding algorithm agrees with the introduced equivalent joint Tanner graph which can be used to fully characterize LDPC codes employed by the sources and relay.Theoretical analysis and numerical simulation show that the proposed scheme with joint iterative decoding can achieve significant cooperation diversity gain.Furthermore,for the relay,compared with the cascade scheme,the proposed scheme has much lower complexity of LDPC-encoding and is easier to be implemented in the hardware with similar bit error rate(BER)performance.
基金the National Natural Science Foundation of China(Nos.61401164,61471131 and 61201145)the Natural Science Foundation of Guangdong Province(No.2014A030310308)
摘要In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are derived by permuting the matrices of the corresponding RC-LDPC block codes,are systematic and have maximum encoding memory.Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation(BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels(BI-AWGNCs).
基金National Mobile Communication Research Laboratory,Southeast University(No.W200704),ChinaNatural Science foundation of Jiangsu Province (No.BK2006188),ChinaQuebec-China Joint Research Foundation by McGill University,Montreal,Quebec,Canada
摘要Two modified BP algorithms related to vertical and horizontal processes are proposed to accelerate iterative low-density parity- check (LDPC) decoding over an additive white Gaussian noise (AWGN) channel, where the newly updated extrinsic information is immediately used in the current decoding round. Theoretical analysis and simulation results demonstrate that both the modified approaches provide significant performance improvements over the traditional BP algorithm with almost no additional decoding complexity. The proposed algorithm with modified horizontal process offers even better performance than another algorithm with the modified horizontal process. The two modified BP algorithms are very promising in practical communications since both can achieve an excellent trade-off between the performance and decoding complexity.
基金Supported by the Open Research Fund of National Moblie Communications Research Laboratory of Southeast Uni-versity (No. W200704)
摘要In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destination which is in accordance with the corresponding joint Tanner graph characterizing two different component LDPC codes used by the source and relay in ideal and non-ideal relay cooperations. The theoretical analysis and simulations show that the coded cooperation scheme obviously outperforms the coded non-cooperation one under the same code rate and decoding complex. The significant performance improvement can be virtually credited to the additional mutual exchange of the extrinsic information resulted by the LDPC code employed by the source and its counterpart used by the relay in both ideal and non-ideal cooperations.
基金This work is partially supported by the National Natural Science Foundation of China(No.61571004)the Shanghai Natural Science Foundation(No.17ZR1429100)+2 种基金the Science and Technology Innovation Program of Shanghai(No.115DZ1100400)Fujian Science and Technology Plan STS Program(2017T3009)the Scientific Instrument Developing Project of the Chinese Academy of Sciences(No.YJKYYQ20170074).
摘要As an effective error correction technology,the Low Density Parity Check Code(LDPC)has been researched and applied by many scholars.Meanwhile,LDPC codes have some prominent performances,which involves close to the Shannon limit,achieving a higher bit rate and a fast decoding.However,whether these excellent characteristics are suitable for the resource-constrained Wireless Sensor Network(WSN),it seems to be seldom concerned.In this article,we review the LDPC code’s structure brief.ly,and them classify and summarize the LDPC codes’construction and decoding algorithms,finally,analyze the applications of LDPC code for WSN.We believe that our contributions will be able to facilitate the application of LDPC code in WSN.