The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Toshiyuki Abe - One of the best experts on this subject based on the ideXlab platform.
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commutant of mathcal l _ widehat mathfrak sl _2 4 0 in the Cyclic Permutation orbifold of mathcal l _ widehat mathfrak sl _2 1 0 otimes 4
arXiv: Quantum Algebra, 2014Co-Authors: Toshiyuki Abe, Hiromichi YamadaAbstract:We study the commutant of the vertex operator algebra $\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(4,0)$ in the Cyclic Permutation orbifold model $(\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(1,0)^{\otimes 4})^\tau$ with $\tau=(1\,2\,3\,4)$. It is shown that the commutant is isomorphic to a ${\mathbb Z}_2\times{\mathbb Z}_2$-orbifold model of a tensor product of two lattice type vertex operator algebras of rank one.
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c 2 cofiniteness of 2 Cyclic Permutation orbifold models
Communications in Mathematical Physics, 2013Co-Authors: Toshiyuki AbeAbstract:In this article, we consider Permutation orbifold models of C 2-cofinite vertex operator algebras of CFT type. We show the C 2-cofiniteness of the 2-Cyclic Permutation orbifold model \({(V \otimes V)^{S_2} }\) for an arbitrary C 2-cofinite simple vertex operator algebra V of CFT type. We also give a proof of the C 2-cofiniteness of a \({\mathbb{Z}_{2}}\) -orbifold model \({V_{L}^{+}}\) of the lattice vertex operator algebra V L associated with a rank one positive definite even lattice L by using our result and the C 2-cofiniteness of V L .
Keping Long - One of the best experts on this subject based on the ideXlab platform.
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circular shift linear network codes with arbitrary odd block lengths
IEEE Transactions on Communications, 2019Co-Authors: Qifu Tyler Sun, Hanqi Tang, Xiaolong Yang, Keping LongAbstract:Circular-shift linear network coding (LNC) is a class of vector LNC with low encoding and decoding complexities, and with local encoding kernels chosen from Cyclic Permutation matrices. When $L$ is a prime with primitive root 2, it was recently shown that a scalar linear solution over GF( $2^{L-1}$ ) induces an $L$ -dimensional circular-shift linear solution at rate $(L-1)/L$ . In this paper, we prove that for arbitrary odd $L$ , every scalar linear solution over GF( $2^{m_{L}}$ ), where $m_{L}$ refers to the multiplicative order of 2 modulo $L$ , can induce an $L$ -dimensional circular-shift linear solution at a certain rate. Based on the generalized connection, we further prove that for such $L$ with $m_{L}$ beyond a threshold, every multicast network has an $L$ -dimensional circular-shift linear solution at rate $\phi (L)/L$ , where $\phi (L)$ is the Euler’s totient function of $L$ . An efficient algorithm for constructing such a solution is designed. Finally, we prove that every multicast network is asymptotically circular-shift linearly solvable.
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circular shift linear network coding
IEEE Transactions on Information Theory, 2019Co-Authors: Hanqi Tang, Zongpeng Li, Xiaolong Yang, Keping LongAbstract:We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions. Formulated as a special vector linear code over GF(2), an $L$ -dimensional circular-shift linear code of degree $\delta $ restricts its local encoding kernels to be the summation of at most $\delta $ Cyclic Permutation matrices of size $L$ . We show that on a general network, for a certain block length $L$ , every scalar linear solution over GF( $2^{L-1}$ ) can induce an $L$ -dimensional circular-shift linear solution with 1-bit redundancy per-edge transmission. Consequently, specific to a multicast network, such a circular-shift linear solution of an arbitrary degree $\delta $ can be efficiently constructed, which has an interesting complexity tradeoff between encoding and decoding with different choices of $\delta $ . By further proving that circular-shift LNC is insufficient to achieve the exact capacity of certain multicast networks, we show the optimality of the efficiently constructed circular-shift linear solution in the sense that its 1-bit redundancy is inevitable. Finally, both theoretical and numerical analysis imply that with increasing $L$ , a randomly constructed circular-shift linear code has linear solvability behavior comparable to a randomly constructed Permutation-based linear code, but has shorter overheads.
Hanqi Tang - One of the best experts on this subject based on the ideXlab platform.
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circular shift linear network codes with arbitrary odd block lengths
IEEE Transactions on Communications, 2019Co-Authors: Qifu Tyler Sun, Hanqi Tang, Xiaolong Yang, Keping LongAbstract:Circular-shift linear network coding (LNC) is a class of vector LNC with low encoding and decoding complexities, and with local encoding kernels chosen from Cyclic Permutation matrices. When $L$ is a prime with primitive root 2, it was recently shown that a scalar linear solution over GF( $2^{L-1}$ ) induces an $L$ -dimensional circular-shift linear solution at rate $(L-1)/L$ . In this paper, we prove that for arbitrary odd $L$ , every scalar linear solution over GF( $2^{m_{L}}$ ), where $m_{L}$ refers to the multiplicative order of 2 modulo $L$ , can induce an $L$ -dimensional circular-shift linear solution at a certain rate. Based on the generalized connection, we further prove that for such $L$ with $m_{L}$ beyond a threshold, every multicast network has an $L$ -dimensional circular-shift linear solution at rate $\phi (L)/L$ , where $\phi (L)$ is the Euler’s totient function of $L$ . An efficient algorithm for constructing such a solution is designed. Finally, we prove that every multicast network is asymptotically circular-shift linearly solvable.
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circular shift linear network coding
IEEE Transactions on Information Theory, 2019Co-Authors: Hanqi Tang, Zongpeng Li, Xiaolong Yang, Keping LongAbstract:We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions. Formulated as a special vector linear code over GF(2), an $L$ -dimensional circular-shift linear code of degree $\delta $ restricts its local encoding kernels to be the summation of at most $\delta $ Cyclic Permutation matrices of size $L$ . We show that on a general network, for a certain block length $L$ , every scalar linear solution over GF( $2^{L-1}$ ) can induce an $L$ -dimensional circular-shift linear solution with 1-bit redundancy per-edge transmission. Consequently, specific to a multicast network, such a circular-shift linear solution of an arbitrary degree $\delta $ can be efficiently constructed, which has an interesting complexity tradeoff between encoding and decoding with different choices of $\delta $ . By further proving that circular-shift LNC is insufficient to achieve the exact capacity of certain multicast networks, we show the optimality of the efficiently constructed circular-shift linear solution in the sense that its 1-bit redundancy is inevitable. Finally, both theoretical and numerical analysis imply that with increasing $L$ , a randomly constructed circular-shift linear code has linear solvability behavior comparable to a randomly constructed Permutation-based linear code, but has shorter overheads.
Xiaolong Yang - One of the best experts on this subject based on the ideXlab platform.
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circular shift linear network codes with arbitrary odd block lengths
IEEE Transactions on Communications, 2019Co-Authors: Qifu Tyler Sun, Hanqi Tang, Xiaolong Yang, Keping LongAbstract:Circular-shift linear network coding (LNC) is a class of vector LNC with low encoding and decoding complexities, and with local encoding kernels chosen from Cyclic Permutation matrices. When $L$ is a prime with primitive root 2, it was recently shown that a scalar linear solution over GF( $2^{L-1}$ ) induces an $L$ -dimensional circular-shift linear solution at rate $(L-1)/L$ . In this paper, we prove that for arbitrary odd $L$ , every scalar linear solution over GF( $2^{m_{L}}$ ), where $m_{L}$ refers to the multiplicative order of 2 modulo $L$ , can induce an $L$ -dimensional circular-shift linear solution at a certain rate. Based on the generalized connection, we further prove that for such $L$ with $m_{L}$ beyond a threshold, every multicast network has an $L$ -dimensional circular-shift linear solution at rate $\phi (L)/L$ , where $\phi (L)$ is the Euler’s totient function of $L$ . An efficient algorithm for constructing such a solution is designed. Finally, we prove that every multicast network is asymptotically circular-shift linearly solvable.
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circular shift linear network coding
IEEE Transactions on Information Theory, 2019Co-Authors: Hanqi Tang, Zongpeng Li, Xiaolong Yang, Keping LongAbstract:We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions. Formulated as a special vector linear code over GF(2), an $L$ -dimensional circular-shift linear code of degree $\delta $ restricts its local encoding kernels to be the summation of at most $\delta $ Cyclic Permutation matrices of size $L$ . We show that on a general network, for a certain block length $L$ , every scalar linear solution over GF( $2^{L-1}$ ) can induce an $L$ -dimensional circular-shift linear solution with 1-bit redundancy per-edge transmission. Consequently, specific to a multicast network, such a circular-shift linear solution of an arbitrary degree $\delta $ can be efficiently constructed, which has an interesting complexity tradeoff between encoding and decoding with different choices of $\delta $ . By further proving that circular-shift LNC is insufficient to achieve the exact capacity of certain multicast networks, we show the optimality of the efficiently constructed circular-shift linear solution in the sense that its 1-bit redundancy is inevitable. Finally, both theoretical and numerical analysis imply that with increasing $L$ , a randomly constructed circular-shift linear code has linear solvability behavior comparable to a randomly constructed Permutation-based linear code, but has shorter overheads.
Hiromichi Yamada - One of the best experts on this subject based on the ideXlab platform.
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commutant of mathcal l _ widehat mathfrak sl _2 4 0 in the Cyclic Permutation orbifold of mathcal l _ widehat mathfrak sl _2 1 0 otimes 4
arXiv: Quantum Algebra, 2014Co-Authors: Toshiyuki Abe, Hiromichi YamadaAbstract:We study the commutant of the vertex operator algebra $\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(4,0)$ in the Cyclic Permutation orbifold model $(\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(1,0)^{\otimes 4})^\tau$ with $\tau=(1\,2\,3\,4)$. It is shown that the commutant is isomorphic to a ${\mathbb Z}_2\times{\mathbb Z}_2$-orbifold model of a tensor product of two lattice type vertex operator algebras of rank one.
