A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding ...A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].展开更多
Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a...Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.展开更多
Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Freml...Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.展开更多
In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum s...In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.展开更多
In this paper, extracting parallelizatio n from the sum of disjoint products approach is discussed. A general framework of parallelizing disjoint products approach is presented. And a parallel version of the newest...In this paper, extracting parallelizatio n from the sum of disjoint products approach is discussed. A general framework of parallelizing disjoint products approach is presented. And a parallel version of the newest disjoint products algorithm is implemented. The results of testing s how the effect is so good to get linear speedups.展开更多
In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correc...In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correction factors is simply based on estimating the mean square difference (MSD) between the transmitted codeword and the posteriori information of both bit and check node that produced at the MS decoder. Semi-practical tests using software-defined radio (SDR) and specific code simulations show that the proposed quasi-optimal algorithm provides a comparable error performance as Sum-Product (SP) decoding while requiring less complexity.展开更多
Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this ...Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.展开更多
Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theore...Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.展开更多
Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of pa...Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.展开更多
Let Fp be the finite field of p elements with p prime.If A is a subset of Fp and g is an element of F＊p with order ν,then max{｜A ＋ g·A｜,｜A·A｜} （ν/（ν ＋ ｜A｜2） ）1/12｜A｜13/12.
The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic rep...The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic representation of transfer functions. To show this we adopt the topological platform for the circuit analysis and use a recently developed Admittance Method (AM) to achieve the Sum of Tree Products (STP), replacing the determinant and cofactors of the Nodal Admittance Matrix (NAM) of the circuit. To construct a transfer function, we start with a given active circuit and convert all its controlled sources and I/O-ports to nullors. Now, with a solid nullor circuit (passive elements and nullors) we first eliminate the passive elements through AM operations. This produces the STPs. Second, the all-nullor circuit is then used to find the signs or the STPs. Finally, the transfer function (in symbolic, if chosen) is obtained from the ratio between the STPs.展开更多
In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-of...In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.展开更多
基金the National Natural Science Foundation of China(No.10271087).
文摘A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].
基金Supported by the National Natural Science Foundation of China(11061012)Project Supported by Program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning([2011]47)the Guangxi Natural Science Foundation of China(2012GXNSFAA053010)
文摘Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.
文摘Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.
文摘In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.
文摘In this paper, extracting parallelizatio n from the sum of disjoint products approach is discussed. A general framework of parallelizing disjoint products approach is presented. And a parallel version of the newest disjoint products algorithm is implemented. The results of testing s how the effect is so good to get linear speedups.
文摘In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correction factors is simply based on estimating the mean square difference (MSD) between the transmitted codeword and the posteriori information of both bit and check node that produced at the MS decoder. Semi-practical tests using software-defined radio (SDR) and specific code simulations show that the proposed quasi-optimal algorithm provides a comparable error performance as Sum-Product (SP) decoding while requiring less complexity.
基金Supported by National Natural Science Foundation of China (Grant No. 10571073)
文摘Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.
基金Project supported by the National Natural Science Foundation of China(No.11061012)the NaturalScience Foundation of Guangxi Province(No.2012GXNSFAA053010)
文摘Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.
基金supported by National Natural Science Foundation of China (Grant No.11001077)
文摘Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.
基金Supported by National Natural Science Foundation of China(Grant No.11271249)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20120073110059)
文摘Let Fp be the finite field of p elements with p prime.If A is a subset of Fp and g is an element of F＊p with order ν,then max{｜A ＋ g·A｜,｜A·A｜} （ν/（ν ＋ ｜A｜2） ）1/12｜A｜13/12.
文摘The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic representation of transfer functions. To show this we adopt the topological platform for the circuit analysis and use a recently developed Admittance Method (AM) to achieve the Sum of Tree Products (STP), replacing the determinant and cofactors of the Nodal Admittance Matrix (NAM) of the circuit. To construct a transfer function, we start with a given active circuit and convert all its controlled sources and I/O-ports to nullors. Now, with a solid nullor circuit (passive elements and nullors) we first eliminate the passive elements through AM operations. This produces the STPs. Second, the all-nullor circuit is then used to find the signs or the STPs. Finally, the transfer function (in symbolic, if chosen) is obtained from the ratio between the STPs.
文摘In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.
