Q-ary low-density parity-check （Q-LDPC） codes have a better performance than those of the binary low-density parity-check （B-LDPC） codes, at short and medium block lengths, but the decoder of Q-LDPC has more compl...Q-ary low-density parity-check （Q-LDPC） codes have a better performance than those of the binary low-density parity-check （B-LDPC） codes, at short and medium block lengths, but the decoder of Q-LDPC has more complexity. In this article, a new stop criterion is proposed. By analyzing the changes of the maximum posteriori probability of the variable node, the criterion decides whether the iteration of the decoder must be stopped. The simulation results show that the stop criterion can effectively reduce the computation complexity of the Q-LDPC decoder with negligible performance loss.展开更多
Trellis structures of block codes are discussed. L-section trellis structures of some BCH codes are presented. A fast maximum likelihood decoding algorithm for BCH codes is proposed correspondingly, the decoding probl...Trellis structures of block codes are discussed. L-section trellis structures of some BCH codes are presented. A fast maximum likelihood decoding algorithm for BCH codes is proposed correspondingly, the decoding problem of q-ary images of qm-ary block codes is also discussed. The direct-sum partition and the associated decoding algorithms are given for the images.展开更多
In this paper, we considered linear block codes over Rq=Fq+uFq+vFq+uvFq, u2=v2=0,uv=vu where q=pm, m∈N . First we looked at the structure of the ring. It was shown that Rq is neither a finite chain ring nor a princip...In this paper, we considered linear block codes over Rq=Fq+uFq+vFq+uvFq, u2=v2=0,uv=vu where q=pm, m∈N . First we looked at the structure of the ring. It was shown that Rq is neither a finite chain ring nor a principal ideal ring but is a local ring. We then established a generator matrix for the linear block codes and equipped it with a homogeneous weight function. Field codes were then constructed as images of these codes by using a basis of Rq over Fq . Bounds on the minimum Hamming distance of the image codes were then derived. A code meeting such bounds is given as an example.展开更多
Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding...Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that q^s can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis （NB） or Optimal Normal Basis （ONB） is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about 42% to 74% less than φ-ary method. For some elliptic curves, our algorithm is also taster than Mǖller＇s algorithm. In addition, an effective algorithm is provided for finding such integer s.展开更多
The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general...The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.展开更多
文摘Q-ary low-density parity-check （Q-LDPC） codes have a better performance than those of the binary low-density parity-check （B-LDPC） codes, at short and medium block lengths, but the decoder of Q-LDPC has more complexity. In this article, a new stop criterion is proposed. By analyzing the changes of the maximum posteriori probability of the variable node, the criterion decides whether the iteration of the decoder must be stopped. The simulation results show that the stop criterion can effectively reduce the computation complexity of the Q-LDPC decoder with negligible performance loss.
基金National Mobile Communications Key Laboratory at Southeast University(China)
文摘Trellis structures of block codes are discussed. L-section trellis structures of some BCH codes are presented. A fast maximum likelihood decoding algorithm for BCH codes is proposed correspondingly, the decoding problem of q-ary images of qm-ary block codes is also discussed. The direct-sum partition and the associated decoding algorithms are given for the images.
文摘In this paper, we considered linear block codes over Rq=Fq+uFq+vFq+uvFq, u2=v2=0,uv=vu where q=pm, m∈N . First we looked at the structure of the ring. It was shown that Rq is neither a finite chain ring nor a principal ideal ring but is a local ring. We then established a generator matrix for the linear block codes and equipped it with a homogeneous weight function. Field codes were then constructed as images of these codes by using a basis of Rq over Fq . Bounds on the minimum Hamming distance of the image codes were then derived. A code meeting such bounds is given as an example.
基金Supported by the National 973 High Technology Projects (No. G1998030420)
文摘Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that q^s can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis （NB） or Optimal Normal Basis （ONB） is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about 42% to 74% less than φ-ary method. For some elliptic curves, our algorithm is also taster than Mǖller＇s algorithm. In addition, an effective algorithm is provided for finding such integer s.
基金supported by the National Natural Science Foundation of China under Grant No.11171366"the Fundamental Research Funds for the Central Universities"South-Central University for Nationalities under Grant No.CZY12014
文摘The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.
