A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the enco...A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparse parity check matrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.展开更多
In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obta...In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.展开更多
We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful atta...We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful attack of this code are also computed. For multi-sender authentication code,it allows a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message.展开更多
The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensi...The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.展开更多
以磁盘冗余阵列(Redundant Array of Inexpensive Disks,RAID)技术中新出现的P-code编码为主要对象,进行了其构造方法、编码及译码算法的详细分析,并首次运用位矩阵(Binary Distribution Matrix,BDM)的方法分析和研究了P-code码。在此...以磁盘冗余阵列(Redundant Array of Inexpensive Disks,RAID)技术中新出现的P-code编码为主要对象,进行了其构造方法、编码及译码算法的详细分析,并首次运用位矩阵(Binary Distribution Matrix,BDM)的方法分析和研究了P-code码。在此基础上,对当前主要RAID-6编码的扩展即更多磁盘数量的容错问题进行了总结与探讨,提出了P-code等垂直最大距离可分码(Maximum Distance Separable,MDS)的扩展将是该领域未来研究的新方向和难点。展开更多
In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic （QC） low-density parity-check （LDPC） codes. Using the proposed approach one may construct some ne...In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic （QC） low-density parity-check （LDPC） codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.展开更多
文摘A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparse parity check matrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.
文摘In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61179026)the Fundamental Research of the Central Universities of China Civil Aviation University of Science Special(Grant No.3122016L005)
文摘We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful attack of this code are also computed. For multi-sender authentication code,it allows a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message.
文摘The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.
文摘以磁盘冗余阵列(Redundant Array of Inexpensive Disks,RAID)技术中新出现的P-code编码为主要对象,进行了其构造方法、编码及译码算法的详细分析,并首次运用位矩阵(Binary Distribution Matrix,BDM)的方法分析和研究了P-code码。在此基础上,对当前主要RAID-6编码的扩展即更多磁盘数量的容错问题进行了总结与探讨,提出了P-code等垂直最大距离可分码(Maximum Distance Separable,MDS)的扩展将是该领域未来研究的新方向和难点。
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60773085 and 60801051)the NSFC-KOSEF International Collaborative Research Funds (Grant Nos 60811140346 and F01-2008-000-10021-0)
文摘In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic （QC） low-density parity-check （LDPC） codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.
