In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the ...In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the nonzero codewords ofHfim （r, 2） are minimal, where Wmax is the maximum nonzero weight in Ham （r, 2） and Hfim （r, 2）.展开更多
Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal...Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.展开更多
Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long bee...Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions.展开更多
有学者提出了一种在压缩语音编码过程中进行QIM(Quantization Index Modulation)隐写的方法.该方法可用于在G.729A压缩语音流中高隐蔽性地嵌入秘密信息,研究其隐写分析方法很有必要.本文首先分析了QIM隐写对G.729A码流造成的显著性特征...有学者提出了一种在压缩语音编码过程中进行QIM(Quantization Index Modulation)隐写的方法.该方法可用于在G.729A压缩语音流中高隐蔽性地嵌入秘密信息,研究其隐写分析方法很有必要.本文首先分析了QIM隐写对G.729A码流造成的显著性特征变化,发现该种隐写将使码流中LPC滤波器的量化索引(码字)发生转移,并导致码字分布的不均衡性及相关性特性发生改变.本文设计了统计模型,实现了对码字分布特性的量化特征抽取;结合支持向量机,本文构造了用于隐写检测的集成分类器系统.实验结果显示本文方法能够在低于30ms的时间内,获得超过98%的检测准确率,实现了对QIM隐写的快速有效检测.展开更多
文摘In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the nonzero codewords ofHfim （r, 2） are minimal, where Wmax is the maximum nonzero weight in Ham （r, 2） and Hfim （r, 2）.
文摘Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.
基金supported by China Postdoctoral Science Foundation(No.2020M670469)National Key Research and Development Program of China(No.2019YFB1803303,No.2020YFB1806702).
文摘Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions.
文摘有学者提出了一种在压缩语音编码过程中进行QIM(Quantization Index Modulation)隐写的方法.该方法可用于在G.729A压缩语音流中高隐蔽性地嵌入秘密信息,研究其隐写分析方法很有必要.本文首先分析了QIM隐写对G.729A码流造成的显著性特征变化,发现该种隐写将使码流中LPC滤波器的量化索引(码字)发生转移,并导致码字分布的不均衡性及相关性特性发生改变.本文设计了统计模型,实现了对码字分布特性的量化特征抽取;结合支持向量机,本文构造了用于隐写检测的集成分类器系统.实验结果显示本文方法能够在低于30ms的时间内,获得超过98%的检测准确率,实现了对QIM隐写的快速有效检测.
