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
The minimum squared Euclidean distance(MSED) of binary multi-h phase codes is presented. The signal segregation degree(SSD) has been put forward to determine MSED of multi-h phase codes. In order to maximize MSED, SSD...The minimum squared Euclidean distance(MSED) of binary multi-h phase codes is presented. The signal segregation degree(SSD) has been put forward to determine MSED of multi-h phase codes. In order to maximize MSED, SSD should be as large as possible. The necessary and sufficient conditions of maximizing SSD are derived. Finally, SSD and the exact formulae for MSED of binary 2-h phase codes are also presented.展开更多
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved i...The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.展开更多
The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matr...The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.展开更多
Three families of low-density parity-check （LDPC） codes are constructed based on the totally isotropic subspaces of symplectic, unitary, and orthogonal spaces over finite fields, respectively. The minimum distances ...Three families of low-density parity-check （LDPC） codes are constructed based on the totally isotropic subspaces of symplectic, unitary, and orthogonal spaces over finite fields, respectively. The minimum distances of the three families of LDPC codes in some special cases are settled.展开更多
In this paper, we prove that for any integer a (1< a<2n), the code A of|A| = a codewords with minimum Hamming weight is an asymptotic optimal solution forthe minimum average Hamming distance problem posed by Ahl...In this paper, we prove that for any integer a (1< a<2n), the code A of|A| = a codewords with minimum Hamming weight is an asymptotic optimal solution forthe minimum average Hamming distance problem posed by Ahlswede and Katona.展开更多
Ⅰ. INTRODUCTION AND MAIN RESULTS Hermitian codes, which are the particular case of cyclotomic Goppa codes are investigated in [2] and [3], but the results on the minimum distance are incomplete. A Hermitian curve ove...Ⅰ. INTRODUCTION AND MAIN RESULTS Hermitian codes, which are the particular case of cyclotomic Goppa codes are investigated in [2] and [3], but the results on the minimum distance are incomplete. A Hermitian curve over the finite field F_q^2 is the展开更多
By extending the notion of the minimum distance for linear network error correction code(LNEC), this paper introduces the concept of generalized minimum rank distance(GMRD) of variable-rate linear network error correc...By extending the notion of the minimum distance for linear network error correction code(LNEC), this paper introduces the concept of generalized minimum rank distance(GMRD) of variable-rate linear network error correction codes. The basic properties of GMRD are investigated. It is proved that GMRD can characterize the error correction/detection capability of variable-rate linear network error correction codes when the source transmits the messages at several different rates.展开更多
Faster-than-Nyquist(FTN)signaling can improve the spectrum efficiency(SE)of the transmission system.In this paper,we propose a coded modulation FTN(CM-FTN)transmission scheme with precoder and channel shortening(CS)op...Faster-than-Nyquist(FTN)signaling can improve the spectrum efficiency(SE)of the transmission system.In this paper,we propose a coded modulation FTN(CM-FTN)transmission scheme with precoder and channel shortening(CS)optimization to improve bit error rate(BER)performance and reduce the complexity of FTN equalizer.In our proposal,the information rate(IR)or spectral efficiency(SE)is employed and verified as a better performance metric for CM-FTN than the minimum Euclidian distance(MED).The precoder of CM-FTN is optimized for maximizing the IR criterion using the bare-bones particle swarm optimization(BB-PSO)algorithm.Further,a three-carrier CM-FTN system model is used to capture the broadening effect of precoder.Also targeting for the IR maximization,the inter-symbol interference(ISI)length for CS is optimized to reduce the receiver complexity without performance loss.Simulation results demonstrate that our method has a 0.6dB precoding gain compared with the nonprecoding scheme and a maximum of 87.5%of the complexity of FTN equalizer is reduced without BER loss.展开更多
Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) is a bandwidth ef- ficient transmission, where the bit error rate is reduced through the iterative information exchange between the inner demapper and...Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) is a bandwidth ef- ficient transmission, where the bit error rate is reduced through the iterative information exchange between the inner demapper and the outer decoder. The choice of the symbol mapping is the crucial design parameter. This paper indicates that the Harmonic Mean of the Minimum Squared Euclidean (HMMSE) distance is the best criterion for the mapping design. Based on the design criterion of the HMMSE distance, a new search algorithm to find the optimized labeling maps for BICM-ID system is proposed. Numerical results and performance comparison show that the new labeling search method has a low complexity and outperforms other labeling schemes using other design criterion in BICM-ID system, therefore it is an optimized labeling method.展开更多
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.
文摘The minimum squared Euclidean distance(MSED) of binary multi-h phase codes is presented. The signal segregation degree(SSD) has been put forward to determine MSED of multi-h phase codes. In order to maximize MSED, SSD should be as large as possible. The necessary and sufficient conditions of maximizing SSD are derived. Finally, SSD and the exact formulae for MSED of binary 2-h phase codes are also presented.
文摘The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.
文摘The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271004, 11371121, 11471096）.
文摘Three families of low-density parity-check （LDPC） codes are constructed based on the totally isotropic subspaces of symplectic, unitary, and orthogonal spaces over finite fields, respectively. The minimum distances of the three families of LDPC codes in some special cases are settled.
文摘In this paper, we prove that for any integer a (1< a<2n), the code A of|A| = a codewords with minimum Hamming weight is an asymptotic optimal solution forthe minimum average Hamming distance problem posed by Ahlswede and Katona.
文摘Ⅰ. INTRODUCTION AND MAIN RESULTS Hermitian codes, which are the particular case of cyclotomic Goppa codes are investigated in [2] and [3], but the results on the minimum distance are incomplete. A Hermitian curve over the finite field F_q^2 is the
文摘By extending the notion of the minimum distance for linear network error correction code(LNEC), this paper introduces the concept of generalized minimum rank distance(GMRD) of variable-rate linear network error correction codes. The basic properties of GMRD are investigated. It is proved that GMRD can characterize the error correction/detection capability of variable-rate linear network error correction codes when the source transmits the messages at several different rates.
基金This work was supported by National Natural Science Foundation of China(No.61961014).
文摘Faster-than-Nyquist(FTN)signaling can improve the spectrum efficiency(SE)of the transmission system.In this paper,we propose a coded modulation FTN(CM-FTN)transmission scheme with precoder and channel shortening(CS)optimization to improve bit error rate(BER)performance and reduce the complexity of FTN equalizer.In our proposal,the information rate(IR)or spectral efficiency(SE)is employed and verified as a better performance metric for CM-FTN than the minimum Euclidian distance(MED).The precoder of CM-FTN is optimized for maximizing the IR criterion using the bare-bones particle swarm optimization(BB-PSO)algorithm.Further,a three-carrier CM-FTN system model is used to capture the broadening effect of precoder.Also targeting for the IR maximization,the inter-symbol interference(ISI)length for CS is optimized to reduce the receiver complexity without performance loss.Simulation results demonstrate that our method has a 0.6dB precoding gain compared with the nonprecoding scheme and a maximum of 87.5%of the complexity of FTN equalizer is reduced without BER loss.
基金Supported by the National Natural Science Foundation of China (No.60472104).
文摘Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) is a bandwidth ef- ficient transmission, where the bit error rate is reduced through the iterative information exchange between the inner demapper and the outer decoder. The choice of the symbol mapping is the crucial design parameter. This paper indicates that the Harmonic Mean of the Minimum Squared Euclidean (HMMSE) distance is the best criterion for the mapping design. Based on the design criterion of the HMMSE distance, a new search algorithm to find the optimized labeling maps for BICM-ID system is proposed. Numerical results and performance comparison show that the new labeling search method has a low complexity and outperforms other labeling schemes using other design criterion in BICM-ID system, therefore it is an optimized labeling method.
