When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum sig...When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.展开更多
It has been shown that quasi orthogonal space time block code (QOSTBC) can achieve high transmission rate with partial diversity. In this paper, a QOSTBC concatenating Bose-Chaudhuri-Hocquenghem (BCH) code structure i...It has been shown that quasi orthogonal space time block code (QOSTBC) can achieve high transmission rate with partial diversity. In this paper, a QOSTBC concatenating Bose-Chaudhuri-Hocquenghem (BCH) code structure is presented. At the receiver, pairwise detection and error correction are first implemented. The decoded data are regrouped. Parallel interference cancellation (PIC) and dual orthogonal space time block code (OSTBC) decoding are deployed to the regrouped data. The pure concatenated scheme is shown to have higher diversity order and better error performance at high signal-to-noise ratio (SNR) scenario than both QOSTBC and OSTBC schemes. The PIC and dual OSTBC decoding algorithm can further obtain approximate 1.2 dB gains than the pure concatenated scheme at 10-6 bit error probability.展开更多
Soft-decision decoding of BCH code in the global navigation satellite system( GNSS) is investigated in order to improve the performance of traditional hard-decision decoding. Using the nice structural properties of BC...Soft-decision decoding of BCH code in the global navigation satellite system( GNSS) is investigated in order to improve the performance of traditional hard-decision decoding. Using the nice structural properties of BCH code,a soft-decision decoding scheme is proposed. It is theoretically shown that the proposed scheme exactly performs maximum-likelihood( ML) decoding,which means the decoding performance is optimal. Moreover,an efficient implementation method of the proposed scheme is designed based on Viterbi algorithm. Simulation results show that the performance of the proposed soft-decision ML decoding scheme is significantly improved compared with the traditional hard-decision decoding method at the expense of moderate complexity increase.展开更多
In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic f...In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic feature under the condition of the frame length known. And then candidate polynomials are achieved which meet the restrictions. Among the candidate polynomials, the most optimal polynomial is selected based on the minimum rule of the weights sum of the syndromes. Finally, the best polynomial was factorized to get the generator polynomial recognized. Simulation results show that the method has strong capability of anti-random bit error. Besides, the algorithm proposed is very simple, so it is very practical for hardware im-plementation.展开更多
It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its des...It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.展开更多
In this paper, only narrow-sense primitive BCH codes over GF(q) are considered. A formula, that can be used in many cases, is first presented for computing the dimension of BCH codes. It improves the result given by M...In this paper, only narrow-sense primitive BCH codes over GF(q) are considered. A formula, that can be used in many cases, is first presented for computing the dimension of BCH codes. It improves the result given by MacWilliams and Sloane in 1977. A new method for finding the dimension of all types of BCH codes is proposed. In second part, it is proved that the BCH bound is the leader of some cyclotomic coset, and we guess that the minimum distance for any BCH code is also the leader of some cyclotomic coset.展开更多
Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlarge...Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlargement of CSS codes applied to nonnarrow-sense BCH codes.The second one is derived from the method of defining sets of classical cyclic codes.The asymmetric quantum BCH codes and subsystem BCH codes here have better parameters than the ones available in the literature.展开更多
本文面向高可靠低时延通信(High-Reliability and Low-Latency Communication,HRLLC)场景的实际需求,提出了一种基于BCH(Bose,Chaudhuri and Hocquenghem,BCH)码的双向叠加编码与低复杂度译码方案.编码方面,采用BCH码作为成分码,基于双...本文面向高可靠低时延通信(High-Reliability and Low-Latency Communication,HRLLC)场景的实际需求,提出了一种基于BCH(Bose,Chaudhuri and Hocquenghem,BCH)码的双向叠加编码与低复杂度译码方案.编码方面,采用BCH码作为成分码,基于双向叠加编码传输(Twisted-Pair Superposition Transmission,TPST)框架,构造了双向叠加BCH(TPST-BCH)码:上层BCH码字经随机变换后叠加至下层BCH码字,叠加版本进一步交织并反馈叠加至上层BCH码字,实现码长扩展与可靠性提升.译码方面,基于串行干扰消除思想,结合局部约束顺序统计译码(Ordered Statistics Decoding with Local Constraints,LC-OSD),先对上层码字生成一系列候选,给定上层候选后对下层码字进行LC-OSD译码,并最终选取后验概率最大的候选作为译码输出.为降低复杂度,我们提出了针对译码的提前终止设计,包括层内提前终止(用于提前终止层内LC-OSD搜索)和跨层提前终止(用于跳过某个上层码字给定后的整个下层LC-OSD搜索).结果显示,所提终止设计可以极大降低搜索次数,且几乎不损失性能.与现有编码方案相比,所提TPST-BCH码(采用所提译码)误帧率优于同码长码率的BCH码(采用LC-OSD算法)、5G LDPC(Low Density Parity Check)码(采用置信传播译码),与5G Polar码(采用串行干扰消除列表译码)误帧率相当或稍优,但在中高信噪比区域相对于5G Polar码具有更低的译码操作数和译码时延.展开更多
This paper establishes a resilient concatenated coding platform for Orthogonal Frequency Division Multiplexing (OFDM) with Quadrature Amplitude Modulation (QAM) over Additive White Gaussian Noise (AWGN) channel. At th...This paper establishes a resilient concatenated coding platform for Orthogonal Frequency Division Multiplexing (OFDM) with Quadrature Amplitude Modulation (QAM) over Additive White Gaussian Noise (AWGN) channel. At the Forward Error Correction (FEC) coding unit, our proposed concatenated coding scheme utilizes standard type of BCH as external coding and LDPC as inner coding. In this scheme, Interleaver inclusion is seen as a catalyst to enhance the systems performance.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 60472018, and the Foundation of National Laboratory for Modern Communications
文摘When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.
基金National Natural Science Foundation of China(No.31003052)Henan University of Technology PhD Fund,China(No.2010BS025)
文摘It has been shown that quasi orthogonal space time block code (QOSTBC) can achieve high transmission rate with partial diversity. In this paper, a QOSTBC concatenating Bose-Chaudhuri-Hocquenghem (BCH) code structure is presented. At the receiver, pairwise detection and error correction are first implemented. The decoded data are regrouped. Parallel interference cancellation (PIC) and dual orthogonal space time block code (OSTBC) decoding are deployed to the regrouped data. The pure concatenated scheme is shown to have higher diversity order and better error performance at high signal-to-noise ratio (SNR) scenario than both QOSTBC and OSTBC schemes. The PIC and dual OSTBC decoding algorithm can further obtain approximate 1.2 dB gains than the pure concatenated scheme at 10-6 bit error probability.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61271423)
文摘Soft-decision decoding of BCH code in the global navigation satellite system( GNSS) is investigated in order to improve the performance of traditional hard-decision decoding. Using the nice structural properties of BCH code,a soft-decision decoding scheme is proposed. It is theoretically shown that the proposed scheme exactly performs maximum-likelihood( ML) decoding,which means the decoding performance is optimal. Moreover,an efficient implementation method of the proposed scheme is designed based on Viterbi algorithm. Simulation results show that the performance of the proposed soft-decision ML decoding scheme is significantly improved compared with the traditional hard-decision decoding method at the expense of moderate complexity increase.
文摘In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic feature under the condition of the frame length known. And then candidate polynomials are achieved which meet the restrictions. Among the candidate polynomials, the most optimal polynomial is selected based on the minimum rule of the weights sum of the syndromes. Finally, the best polynomial was factorized to get the generator polynomial recognized. Simulation results show that the method has strong capability of anti-random bit error. Besides, the algorithm proposed is very simple, so it is very practical for hardware im-plementation.
基金Supported by the National Natural Science Foundation of China (No.60403004)the Outstanding Youth Foundation of China (No.0612000500)
文摘It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.
文摘In this paper, only narrow-sense primitive BCH codes over GF(q) are considered. A formula, that can be used in many cases, is first presented for computing the dimension of BCH codes. It improves the result given by MacWilliams and Sloane in 1977. A new method for finding the dimension of all types of BCH codes is proposed. In second part, it is proved that the BCH bound is the leader of some cyclotomic coset, and we guess that the minimum distance for any BCH code is also the leader of some cyclotomic coset.
基金supported by the National High Technology Research and Development Program of China (Grant No. 2011AA010803)the National Natural Science Foundation of China (Grant No. 60403004)the Outstanding Youth Foundation of Henan Province (Grant No. 0612000500)
文摘Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlargement of CSS codes applied to nonnarrow-sense BCH codes.The second one is derived from the method of defining sets of classical cyclic codes.The asymmetric quantum BCH codes and subsystem BCH codes here have better parameters than the ones available in the literature.
文摘本文面向高可靠低时延通信(High-Reliability and Low-Latency Communication,HRLLC)场景的实际需求,提出了一种基于BCH(Bose,Chaudhuri and Hocquenghem,BCH)码的双向叠加编码与低复杂度译码方案.编码方面,采用BCH码作为成分码,基于双向叠加编码传输(Twisted-Pair Superposition Transmission,TPST)框架,构造了双向叠加BCH(TPST-BCH)码:上层BCH码字经随机变换后叠加至下层BCH码字,叠加版本进一步交织并反馈叠加至上层BCH码字,实现码长扩展与可靠性提升.译码方面,基于串行干扰消除思想,结合局部约束顺序统计译码(Ordered Statistics Decoding with Local Constraints,LC-OSD),先对上层码字生成一系列候选,给定上层候选后对下层码字进行LC-OSD译码,并最终选取后验概率最大的候选作为译码输出.为降低复杂度,我们提出了针对译码的提前终止设计,包括层内提前终止(用于提前终止层内LC-OSD搜索)和跨层提前终止(用于跳过某个上层码字给定后的整个下层LC-OSD搜索).结果显示,所提终止设计可以极大降低搜索次数,且几乎不损失性能.与现有编码方案相比,所提TPST-BCH码(采用所提译码)误帧率优于同码长码率的BCH码(采用LC-OSD算法)、5G LDPC(Low Density Parity Check)码(采用置信传播译码),与5G Polar码(采用串行干扰消除列表译码)误帧率相当或稍优,但在中高信噪比区域相对于5G Polar码具有更低的译码操作数和译码时延.
文摘This paper establishes a resilient concatenated coding platform for Orthogonal Frequency Division Multiplexing (OFDM) with Quadrature Amplitude Modulation (QAM) over Additive White Gaussian Noise (AWGN) channel. At the Forward Error Correction (FEC) coding unit, our proposed concatenated coding scheme utilizes standard type of BCH as external coding and LDPC as inner coding. In this scheme, Interleaver inclusion is seen as a catalyst to enhance the systems performance.
