Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of...Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.展开更多
This paper presents an intelligent protograph construction algorithm.Protograph LDPC codes have shown excellent error correction performance and play an important role in wireless communications.Random search or manua...This paper presents an intelligent protograph construction algorithm.Protograph LDPC codes have shown excellent error correction performance and play an important role in wireless communications.Random search or manual construction are often used to obtain a good protograph,but the efficiency is not high enough and many experience and skills are needed.In this paper,a fast searching algorithm is proposed using the convolution neural network to predict the iterative decoding thresholds of protograph LDPC codes effectively.A special input data transformation rule is applied to provide stronger generalization ability.The proposed algorithm converges faster than other algorithms.The iterative decoding threshold of the constructed protograph surpasses greedy algorithm and random search by about 0.53 dB and 0.93 dB respectively under 100 times of density evolution.Simulation results show that quasi-cyclic LDPC(QC-LDPC)codes constructed from the proposed algorithm have competitive performance compared to other papers.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
In this paper,it has proposed a realtime implementation of low-density paritycheck(LDPC) decoder with less complexity used for satellite communication on FPGA platform.By adopting a(2048.4096)irregular quasi-cyclic(QC...In this paper,it has proposed a realtime implementation of low-density paritycheck(LDPC) decoder with less complexity used for satellite communication on FPGA platform.By adopting a(2048.4096)irregular quasi-cyclic(QC) LDPC code,the proposed partly parallel decoding structure balances the complexity between the check node unit(CNU) and the variable node unit(VNU) based on min-sum(MS) algorithm,thereby achieving less Slice resources and superior clock performance.Moreover,as a lookup table(LUT) is utilized in this paper to search the node message stored in timeshare memory unit,it is simple to reuse and save large amount of storage resources.The implementation results on Xilinx FPGA chip illustrate that,compared with conventional structure,the proposed scheme can achieve at last 28.6%and 8%cost reduction in RAM and Slice respectively.The clock frequency is also increased to 280 MHz without decoding performance deterioration and convergence speed reduction.展开更多
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 intr...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, we propose a construction algorithm of LDPC codes, to which a constraint condition is added in the Progressive Edge-Growth (PEG) algorithm. The constraint condition can guarantee that for our constructed LDPC codes, the sets of all the variable nodes connected to the consecutive layers do not share any common variable node, which can avoid the memory access conflicts. Simulation results show that the performance of our constructed LDPC codes is close to the several other LDPC codes adopted in wireless standards. Moreover, compared with the decoder for IEEE 802. 16e LDPC codes, the throughput of our LDPC decoder has large improvement, while the chip resource consumption is unchanged. Thus, our constructed LDPC codes can be adopted in the high-speed transmission.展开更多
In this paper, we present a Joint Source-Channel Decoding algorithm (JSCD) for Low-Density Parity Check (LDPC) codes by modifying the Sum-Product Algorithm (SPA) to account for the source redun-dancy, which results fr...In this paper, we present a Joint Source-Channel Decoding algorithm (JSCD) for Low-Density Parity Check (LDPC) codes by modifying the Sum-Product Algorithm (SPA) to account for the source redun-dancy, which results from the neighbouring Huffman coded bits. Simulations demonstrate that in the presence of source redundancy, the proposed algorithm gives better performance than the Separate Source and Channel Decoding algorithm (SSCD).展开更多
Genetic algorithms are successfully used for decoding some classes of error correcting codes, and offer very good performances for solving large optimization problems. This article proposes a new decoder based on Seri...Genetic algorithms are successfully used for decoding some classes of error correcting codes, and offer very good performances for solving large optimization problems. This article proposes a new decoder based on Serial Genetic Algorithm Decoder (SGAD) for decoding Low Density Parity Check (LDPC) codes. The results show that the proposed algorithm gives large gains over sum-product decoder, which proves its efficiency.展开更多
<div style="text-align:justify;"> Low-density parity-check code (LDPC) not only has good performance approaching the Shannon limit, but also has low decoding complexity and flexible structure. It is a ...<div style="text-align:justify;"> Low-density parity-check code (LDPC) not only has good performance approaching the Shannon limit, but also has low decoding complexity and flexible structure. It is a research hot-spot in the field of channel coding in recent years and has a wide range of application prospects in optical communication systems. In this paper, the decoding aspects and performance of LDPC codes are analyzed and compared according to the bit error rate (BER) of LDPC codes. The computer simulation was carried out under additive white Gaussian noise (AWGN) channel and binary phase shift keying (BPSK) modulation. Through theoretical analysis and simulation results, this paper explores the way of multi-rate LDPC decoding. </div>展开更多
A hybrid decoding algorithm is proposed for nonbinary low-density parity-check(LDPC)codes,which combines the weighted symbol-flipping(WSF)algorithm with the fast Fourier transform q-ary sum-product algorithm(FFT-QSPA)...A hybrid decoding algorithm is proposed for nonbinary low-density parity-check(LDPC)codes,which combines the weighted symbol-flipping(WSF)algorithm with the fast Fourier transform q-ary sum-product algorithm(FFT-QSPA).The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm.If the lowcomplexity WSF algorithm is failed,the second stage FFT-QSPA is activated as a switching strategy.Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.展开更多
利用变量节点符号可靠度在迭代过程中的分布特征,提出了一种基于可靠度差值特征的自适应判决多元低密度奇偶校验(Low Density Parity Check, LDPC)译码算法。整个迭代过程划分为两个阶段,针对不同阶段节点可靠度的差值特征分别采用不同...利用变量节点符号可靠度在迭代过程中的分布特征,提出了一种基于可靠度差值特征的自适应判决多元低密度奇偶校验(Low Density Parity Check, LDPC)译码算法。整个迭代过程划分为两个阶段,针对不同阶段节点可靠度的差值特征分别采用不同的判决策略:前期阶段,采用传统的基于最大可靠度的判决策略;后期阶段,根据最大、次大可靠度之间的差值特征,设计自适应的码元符号判决策略。仿真结果表明,所提算法在相当的译码复杂度前提下,能获得0.15~0.4 dB的性能增益。同时,对于列重较小的LDPC码,具有更低的译码错误平层。展开更多
In this paper a low-density pairwise check(LDPC) coded three-way relay system is considered, where three user nodes desire to exchange messages with the help of one relay node. Since physical-layer network coding is a...In this paper a low-density pairwise check(LDPC) coded three-way relay system is considered, where three user nodes desire to exchange messages with the help of one relay node. Since physical-layer network coding is applied, two time slots are sufficient for one round information exchange. In this paper, we present a decode-and-forward(DF) scheme based on joint LDPC decoding for three-way relay channels, where relay decoder partially decodes the network code rather than fully decodes all the user messages. Simulation results show that the new DF scheme considerably outperforms other common schemes in three-way relay fading channels.展开更多
In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDP...In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.展开更多
With the development of manufacture technology, the multi-level cell(MLC)technique dramatically increases the storage density of NAND flash memory. As the result,cell-to-cell interference(CCI) becomes more serious and...With the development of manufacture technology, the multi-level cell(MLC)technique dramatically increases the storage density of NAND flash memory. As the result,cell-to-cell interference(CCI) becomes more serious and hence causes an increase in the raw bit error rate of data stored in the cells.Recently, low-density parity-check(LDPC)codes have appeared to be a promising solution to combat the interference of MLC NAND flash memory. However, the decoding complexity of the sum-product algorithm(SPA) is extremely high. In this paper, to improve the accuracy of the log likelihood ratio(LLR) information of each bit in each NAND flash memory cell, we adopt a non-uniform detection(N-UD) which uses the average maximum mutual information to determine the value of the soft-decision reference voltages.Furthermore, with an aim to reduce the decoding complexity and improve the decoding performance, we propose a modified soft reliabilitybased iterative majority-logic decoding(MSRBI-MLGD) algorithm, which uses a non-uniform quantizer based on power function to decode LDPC codes. Simulation results show that our design can offer a desirable trade-off between the performance and complexity for high-column-weight LDPC-coded MLC NAND flash memory.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 frequency/timing 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
This paper presents a low complexity optimized algorithm for design of bilayer lengthened LDPC(BL-LDPC) code for decode-and-forward relay system.The design is performed over the expanded graph of the BL-LDPC code,whic...This paper presents a low complexity optimized algorithm for design of bilayer lengthened LDPC(BL-LDPC) code for decode-and-forward relay system.The design is performed over the expanded graph of the BL-LDPC code,which consists of the original bilayer graph and the extra added relaygenerated parity check bits.To build up our proposed optimized algorithm,we present a modified Gaussian approximation algorithm for the expanded structure of the BL-LDPC code.Then using the proposed optimized algorithm,we find the optimum overall expanded graph of the BL-LDPC code.Simulation results show that the BL-LDPC codes obtained by our proposed optimized algorithm have excellent bit-error-rate performances and small gaps between the convergence thresholds and the theoretical limits when transmitted over the additive white Gaussian noise channels.展开更多
Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of...Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of LDPC codes is their relatively lower decoding complexity compared with turbo codes,while the disadvantage is its higher encoding complexity.In this paper,a new ap- proach is first proposed to construct high performance irregular systematic LDPC codes based on sparse generator matrix,which can significantly reduce the encoding complexity under the same de- coding complexity as that of regular or irregular LDPC codes defined by traditional sparse parity-check matrix.Then,the proposed generator-based systematic irregular LDPC codes are adopted as con- stituent block codes in rows and columns to design a new kind of product codes family,which also can be interpreted as irregular LDPC codes characterized by graph and thus decoded iteratively.Finally, the performance of the generator-based LDPC codes and the resultant product codes is investigated over an Additive White Gaussian Noise (AWGN) and also compared with the conventional LDPC codes under the same conditions of decoding complexity and channel noise.展开更多
In this paper, A Belief Propagation concatenated Orderd-Statistic Decoder (BP-OSD) based on accumulated Log-Likelihood Ratio (LLR) is proposed for medium and short lengths Low Density Parity-Check (LDPC) codes coded B...In this paper, A Belief Propagation concatenated Orderd-Statistic Decoder (BP-OSD) based on accumulated Log-Likelihood Ratio (LLR) is proposed for medium and short lengths Low Density Parity-Check (LDPC) codes coded Bit-Interleaved Coded Modulation (BICM) systems. The accumulated soft output values delivered by every BP iteration are used as reliability values of Soft-Input Soft-Output OSD (SISO-OSD) decoder and the soft output of SISO-OSD is used as a priori probabilities of the demodulator for the next iteration. Simulation results show that this improved algorithm achieves noticeable performance gain with only modest increase in computation complexity.展开更多
基金supported in part by National Nature Science Foundation of China under Grant No.61471286,No.61271004the Fundamental Research Funds for the Central Universitiesthe open research fund of Key Laboratory of Information Coding and Transmission,Southwest Jiaotong University(No.2010-03)
文摘Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.
基金supported in part with the Project on the Industry Key Technologies of Jiangsu Province(No.BE2017153)the Industry-University-Research Fund of ZTE Corporation.
文摘This paper presents an intelligent protograph construction algorithm.Protograph LDPC codes have shown excellent error correction performance and play an important role in wireless communications.Random search or manual construction are often used to obtain a good protograph,but the efficiency is not high enough and many experience and skills are needed.In this paper,a fast searching algorithm is proposed using the convolution neural network to predict the iterative decoding thresholds of protograph LDPC codes effectively.A special input data transformation rule is applied to provide stronger generalization ability.The proposed algorithm converges faster than other algorithms.The iterative decoding threshold of the constructed protograph surpasses greedy algorithm and random search by about 0.53 dB and 0.93 dB respectively under 100 times of density evolution.Simulation results show that quasi-cyclic LDPC(QC-LDPC)codes constructed from the proposed algorithm have competitive performance compared to other papers.
文摘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.
文摘In this paper,it has proposed a realtime implementation of low-density paritycheck(LDPC) decoder with less complexity used for satellite communication on FPGA platform.By adopting a(2048.4096)irregular quasi-cyclic(QC) LDPC code,the proposed partly parallel decoding structure balances the complexity between the check node unit(CNU) and the variable node unit(VNU) based on min-sum(MS) algorithm,thereby achieving less Slice resources and superior clock performance.Moreover,as a lookup table(LUT) is utilized in this paper to search the node message stored in timeshare memory unit,it is simple to reuse and save large amount of storage resources.The implementation results on Xilinx FPGA chip illustrate that,compared with conventional structure,the proposed scheme can achieve at last 28.6%and 8%cost reduction in RAM and Slice respectively.The clock frequency is also increased to 280 MHz without decoding performance deterioration and convergence speed reduction.
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
文摘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, we propose a construction algorithm of LDPC codes, to which a constraint condition is added in the Progressive Edge-Growth (PEG) algorithm. The constraint condition can guarantee that for our constructed LDPC codes, the sets of all the variable nodes connected to the consecutive layers do not share any common variable node, which can avoid the memory access conflicts. Simulation results show that the performance of our constructed LDPC codes is close to the several other LDPC codes adopted in wireless standards. Moreover, compared with the decoder for IEEE 802. 16e LDPC codes, the throughput of our LDPC decoder has large improvement, while the chip resource consumption is unchanged. Thus, our constructed LDPC codes can be adopted in the high-speed transmission.
文摘In this paper, we present a Joint Source-Channel Decoding algorithm (JSCD) for Low-Density Parity Check (LDPC) codes by modifying the Sum-Product Algorithm (SPA) to account for the source redun-dancy, which results from the neighbouring Huffman coded bits. Simulations demonstrate that in the presence of source redundancy, the proposed algorithm gives better performance than the Separate Source and Channel Decoding algorithm (SSCD).
文摘Genetic algorithms are successfully used for decoding some classes of error correcting codes, and offer very good performances for solving large optimization problems. This article proposes a new decoder based on Serial Genetic Algorithm Decoder (SGAD) for decoding Low Density Parity Check (LDPC) codes. The results show that the proposed algorithm gives large gains over sum-product decoder, which proves its efficiency.
文摘<div style="text-align:justify;"> Low-density parity-check code (LDPC) not only has good performance approaching the Shannon limit, but also has low decoding complexity and flexible structure. It is a research hot-spot in the field of channel coding in recent years and has a wide range of application prospects in optical communication systems. In this paper, the decoding aspects and performance of LDPC codes are analyzed and compared according to the bit error rate (BER) of LDPC codes. The computer simulation was carried out under additive white Gaussian noise (AWGN) channel and binary phase shift keying (BPSK) modulation. Through theoretical analysis and simulation results, this paper explores the way of multi-rate LDPC decoding. </div>
基金Supported by the National High Technology Research and Development Programme of China(No.2009AAJ128,2009AAJ208,2010AA7010422)
文摘A hybrid decoding algorithm is proposed for nonbinary low-density parity-check(LDPC)codes,which combines the weighted symbol-flipping(WSF)algorithm with the fast Fourier transform q-ary sum-product algorithm(FFT-QSPA).The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm.If the lowcomplexity WSF algorithm is failed,the second stage FFT-QSPA is activated as a switching strategy.Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.
基金supported in part by the National Natural Science Foundation of China under Grant 61201187by the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions under Grant YETP0110+2 种基金by the Tsinghua University Initiative Scientific Research Program under Grant 20121088074by the Foundation of Zhejiang Educational Committee under Grant Y201121579by the Visiting Scholar Professional Development Project of Zhejiang Educational Committee under Grant FX2014052
文摘In this paper a low-density pairwise check(LDPC) coded three-way relay system is considered, where three user nodes desire to exchange messages with the help of one relay node. Since physical-layer network coding is applied, two time slots are sufficient for one round information exchange. In this paper, we present a decode-and-forward(DF) scheme based on joint LDPC decoding for three-way relay channels, where relay decoder partially decodes the network code rather than fully decodes all the user messages. Simulation results show that the new DF scheme considerably outperforms other common schemes in three-way relay fading channels.
基金supported in part by National Natural Science Foundation of China under Grants 61372074,91438101,61103143,U1504601,and U1404622Key Scientific and Technological Project of Henan under Grants 162102310589 and 172102310124
文摘In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.
基金supported in part by the NSF of China (61471131, 61771149, 61501126)NSF of Guangdong Province 2016A030310337+1 种基金the open research fund of National Mobile Communications Research Laboratory, Southeast University (No. 2018D02)the Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2017-ZJ022)
文摘With the development of manufacture technology, the multi-level cell(MLC)technique dramatically increases the storage density of NAND flash memory. As the result,cell-to-cell interference(CCI) becomes more serious and hence causes an increase in the raw bit error rate of data stored in the cells.Recently, low-density parity-check(LDPC)codes have appeared to be a promising solution to combat the interference of MLC NAND flash memory. However, the decoding complexity of the sum-product algorithm(SPA) is extremely high. In this paper, to improve the accuracy of the log likelihood ratio(LLR) information of each bit in each NAND flash memory cell, we adopt a non-uniform detection(N-UD) which uses the average maximum mutual information to determine the value of the soft-decision reference voltages.Furthermore, with an aim to reduce the decoding complexity and improve the decoding performance, we propose a modified soft reliabilitybased iterative majority-logic decoding(MSRBI-MLGD) algorithm, which uses a non-uniform quantizer based on power function to decode LDPC codes. Simulation results show that our design can offer a desirable trade-off between the performance and complexity for high-column-weight LDPC-coded MLC NAND flash memory.
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)
文摘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 frequency/timing 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Supported by the National Basic Research Program of China(No.2012CB316100)the National Natural Science Foundation of China(No.61072064,61201140,61301177)
文摘This paper presents a low complexity optimized algorithm for design of bilayer lengthened LDPC(BL-LDPC) code for decode-and-forward relay system.The design is performed over the expanded graph of the BL-LDPC code,which consists of the original bilayer graph and the extra added relaygenerated parity check bits.To build up our proposed optimized algorithm,we present a modified Gaussian approximation algorithm for the expanded structure of the BL-LDPC code.Then using the proposed optimized algorithm,we find the optimum overall expanded graph of the BL-LDPC code.Simulation results show that the BL-LDPC codes obtained by our proposed optimized algorithm have excellent bit-error-rate performances and small gaps between the convergence thresholds and the theoretical limits when transmitted over the additive white Gaussian noise channels.
基金Supported by the National Aeronautical Foundation of Science and Research of China (No.04F52041)the Natural Science Foundation of Jiangsu Province (No.BK2006188).
文摘Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of LDPC codes is their relatively lower decoding complexity compared with turbo codes,while the disadvantage is its higher encoding complexity.In this paper,a new ap- proach is first proposed to construct high performance irregular systematic LDPC codes based on sparse generator matrix,which can significantly reduce the encoding complexity under the same de- coding complexity as that of regular or irregular LDPC codes defined by traditional sparse parity-check matrix.Then,the proposed generator-based systematic irregular LDPC codes are adopted as con- stituent block codes in rows and columns to design a new kind of product codes family,which also can be interpreted as irregular LDPC codes characterized by graph and thus decoded iteratively.Finally, the performance of the generator-based LDPC codes and the resultant product codes is investigated over an Additive White Gaussian Noise (AWGN) and also compared with the conventional LDPC codes under the same conditions of decoding complexity and channel noise.
基金Supported by the National Natural Science Foundation of China (No: 60496311)
文摘In this paper, A Belief Propagation concatenated Orderd-Statistic Decoder (BP-OSD) based on accumulated Log-Likelihood Ratio (LLR) is proposed for medium and short lengths Low Density Parity-Check (LDPC) codes coded Bit-Interleaved Coded Modulation (BICM) systems. The accumulated soft output values delivered by every BP iteration are used as reliability values of Soft-Input Soft-Output OSD (SISO-OSD) decoder and the soft output of SISO-OSD is used as a priori probabilities of the demodulator for the next iteration. Simulation results show that this improved algorithm achieves noticeable performance gain with only modest increase in computation complexity.