Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rat...Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.展开更多
A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the we...A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.展开更多
The QR Code is a 2 dimensional matrix code with high error correction capability. It employs RS codes to generate error correction codewords in encoding and recover errors and damages in decoding. This paper presents ...The QR Code is a 2 dimensional matrix code with high error correction capability. It employs RS codes to generate error correction codewords in encoding and recover errors and damages in decoding. This paper presents several QR Code’s virtues, analyzes RS decoding algorithm and gives a software flow chart of decoding the QR Code with RS decoding algorithm.展开更多
In this paper, we propose a packet-interleaving scheme (PIS) for increasing packet reliability under burst errors in wireless sensor networks (WSN). In a WSN, packet errors could occur due to weak signal strength or i...In this paper, we propose a packet-interleaving scheme (PIS) for increasing packet reliability under burst errors in wireless sensor networks (WSN). In a WSN, packet errors could occur due to weak signal strength or interference. These erroneous packets have to be retransmitted, which will increase network load substantially. The proposed PIS, encoding data using Reed-Solomon (RS) codes, can classify data into two different types: high-reliability-required (HRR) data and non-HRR data. An HRR packet is encoded with a short RS symbol, while a non-HRR packet with a long RS symbol. When an HRR and a non-HRR packet arrive at a sensor, they are interleaved on a symbol-by-symbol basis. Thus, the effect of burst errors (BE) is dispersed and consequently the uncorrectable HRR packets can be reduced. For the purpose of evaluation, two models, the uniform bit-error model (UBEM) and the on-off bit-error model (OBEM), are built to analyze the packet uncorrectable probability. In the evaluation, we first change the lengths of BE, then we vary the shift positions in a BE period, and finally we increase the number of correctable symbols to observe the superiority of the proposed PIS in reducing packet uncorrectable probability.展开更多
Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding proc...Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.展开更多
In this paper, we construct MDS Euclidean self-dual codes which are ex-tended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized...In this paper, we construct MDS Euclidean self-dual codes which are ex-tended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes.展开更多
In this paper,a novel dual-metric,the maximum and minimum Squared Euclidean Distance Increment (SEDI) brought by changing the hard decision symbol,is introduced to measure the reli-ability of the received M-ary Phase ...In this paper,a novel dual-metric,the maximum and minimum Squared Euclidean Distance Increment (SEDI) brought by changing the hard decision symbol,is introduced to measure the reli-ability of the received M-ary Phase Shift Keying (MPSK) symbols over a Rayleigh fading channel. Based on the dual-metric,a Chase-type soft decoding algorithm,which is called erased-Chase algorithm,is developed for Reed-Solomon (RS) coded MPSK schemes. The proposed algorithm treats the unre-liable symbols with small maximum SEDI as erasures,and tests the non-erased unreliable symbols with small minimum SEDI as the Chase-2 algorithm does. By introducing optimality test into the decoding procedure,much more reduction in the decoding complexity can be achieved. Simulation results of the RS(63,42,22)-coded 8-PSK scheme over a Rayleigh fading channel show that the proposed algorithm provides a very efficient tradeoff between the decoding complexity and the error performance. Finally,an adaptive scheme for the number of erasures is introduced into the decoding algorithm.展开更多
针对实际工程应用中的里德-所罗门(Reed-Solomon,RS)编码识别问题,根据国际空间数据系统咨询委员会(Consultative Committee for Space Data Systems,CCSDS)标准,提出了基于软信息的低复杂度缩短交织RS编码识别算法。利用码字同步算法...针对实际工程应用中的里德-所罗门(Reed-Solomon,RS)编码识别问题,根据国际空间数据系统咨询委员会(Consultative Committee for Space Data Systems,CCSDS)标准,提出了基于软信息的低复杂度缩短交织RS编码识别算法。利用码字同步算法对码字起点和缩短长度进行识别,利用接收到的RS码字计算基于校正子后验概率对数似然比平均值的编码识别特征,对码字的交织深度进行识别;进而利用识别所得的RS码交织深度和缩短长度对接收码字进行解交织和码字填充,识别RS码生成多项式。仿真结果表明,所提算法在信噪比为6.1 dB时正确识别概率即可大于90%,相较传统硬判决识别算法和基于伽罗华域快速傅里叶变换(Galois Field Fourier Transform,GFFT)的谱累积量算法均有显著的性能提升。展开更多
为解决里所(Reed-solomon,RS)编码的低功耗设计,从系统架构、RTL级、门级等不同设计层级进行分析,并在专用集成电路(Application specific integrated circuit,ASIC)设计中加以实践。基于低功耗设计将前端RTL级设计与后端IC设计结合起来...为解决里所(Reed-solomon,RS)编码的低功耗设计,从系统架构、RTL级、门级等不同设计层级进行分析,并在专用集成电路(Application specific integrated circuit,ASIC)设计中加以实践。基于低功耗设计将前端RTL级设计与后端IC设计结合起来,研究能实现RS编码功能的芯片。在系统架构层,针对RS编码算法中伽罗华域的乘法运算在硬件实现时存在数据运算量大、消耗功耗大等问题,提出基于乘法器因子矩阵的方法对RS编码算法进行优化,通过将乘法运算转化为减法运算等方式减少数据运算量,从而降低功耗。在RTL级和门级层面,分别在逻辑综合和后端实现中加以约束来实现低功耗设计,总体功耗可以降低60%左右。解决了因IC芯片功耗过高导致芯片性能下降,从而影响芯片正常工作等问题,为集成电路工艺提供了新的发展方向。展开更多
基金This work was supported in part by National Natural Science Foundation of China(No.61671324)the Director’s Funding from Pilot National Laboratory for Marine Science and Technology(Qingdao)(QNLM201712).
文摘Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.
基金Sponsored by the Ministerial Level Advanced Research Foundation (20304)
文摘A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.
文摘The QR Code is a 2 dimensional matrix code with high error correction capability. It employs RS codes to generate error correction codewords in encoding and recover errors and damages in decoding. This paper presents several QR Code’s virtues, analyzes RS decoding algorithm and gives a software flow chart of decoding the QR Code with RS decoding algorithm.
文摘In this paper, we propose a packet-interleaving scheme (PIS) for increasing packet reliability under burst errors in wireless sensor networks (WSN). In a WSN, packet errors could occur due to weak signal strength or interference. These erroneous packets have to be retransmitted, which will increase network load substantially. The proposed PIS, encoding data using Reed-Solomon (RS) codes, can classify data into two different types: high-reliability-required (HRR) data and non-HRR data. An HRR packet is encoded with a short RS symbol, while a non-HRR packet with a long RS symbol. When an HRR and a non-HRR packet arrive at a sensor, they are interleaved on a symbol-by-symbol basis. Thus, the effect of burst errors (BE) is dispersed and consequently the uncorrectable HRR packets can be reduced. For the purpose of evaluation, two models, the uniform bit-error model (UBEM) and the on-off bit-error model (OBEM), are built to analyze the packet uncorrectable probability. In the evaluation, we first change the lengths of BE, then we vary the shift positions in a BE period, and finally we increase the number of correctable symbols to observe the superiority of the proposed PIS in reducing packet uncorrectable probability.
基金She was with the Department of Mathematics in Wuhan University while writting this paper.
文摘Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.
文摘In this paper, we construct MDS Euclidean self-dual codes which are ex-tended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes.
基金the National Natural Science Foundation of China (No.60272057).
文摘In this paper,a novel dual-metric,the maximum and minimum Squared Euclidean Distance Increment (SEDI) brought by changing the hard decision symbol,is introduced to measure the reli-ability of the received M-ary Phase Shift Keying (MPSK) symbols over a Rayleigh fading channel. Based on the dual-metric,a Chase-type soft decoding algorithm,which is called erased-Chase algorithm,is developed for Reed-Solomon (RS) coded MPSK schemes. The proposed algorithm treats the unre-liable symbols with small maximum SEDI as erasures,and tests the non-erased unreliable symbols with small minimum SEDI as the Chase-2 algorithm does. By introducing optimality test into the decoding procedure,much more reduction in the decoding complexity can be achieved. Simulation results of the RS(63,42,22)-coded 8-PSK scheme over a Rayleigh fading channel show that the proposed algorithm provides a very efficient tradeoff between the decoding complexity and the error performance. Finally,an adaptive scheme for the number of erasures is introduced into the decoding algorithm.
文摘针对实际工程应用中的里德-所罗门(Reed-Solomon,RS)编码识别问题,根据国际空间数据系统咨询委员会(Consultative Committee for Space Data Systems,CCSDS)标准,提出了基于软信息的低复杂度缩短交织RS编码识别算法。利用码字同步算法对码字起点和缩短长度进行识别,利用接收到的RS码字计算基于校正子后验概率对数似然比平均值的编码识别特征,对码字的交织深度进行识别;进而利用识别所得的RS码交织深度和缩短长度对接收码字进行解交织和码字填充,识别RS码生成多项式。仿真结果表明,所提算法在信噪比为6.1 dB时正确识别概率即可大于90%,相较传统硬判决识别算法和基于伽罗华域快速傅里叶变换(Galois Field Fourier Transform,GFFT)的谱累积量算法均有显著的性能提升。
文摘为解决里所(Reed-solomon,RS)编码的低功耗设计,从系统架构、RTL级、门级等不同设计层级进行分析,并在专用集成电路(Application specific integrated circuit,ASIC)设计中加以实践。基于低功耗设计将前端RTL级设计与后端IC设计结合起来,研究能实现RS编码功能的芯片。在系统架构层,针对RS编码算法中伽罗华域的乘法运算在硬件实现时存在数据运算量大、消耗功耗大等问题,提出基于乘法器因子矩阵的方法对RS编码算法进行优化,通过将乘法运算转化为减法运算等方式减少数据运算量,从而降低功耗。在RTL级和门级层面,分别在逻辑综合和后端实现中加以约束来实现低功耗设计,总体功耗可以降低60%左右。解决了因IC芯片功耗过高导致芯片性能下降,从而影响芯片正常工作等问题,为集成电路工艺提供了新的发展方向。
