Search Results - "vector linear network coding"

On Matrix Representation of Extension Field GF(pL) and Its Application in Vector Linear Network Coding by Tang, Hanqi, Liu, Heping, Jin, Sheng, Liu, Wenli, Sun, Qifu

“…For a finite field GF(pL) with prime p and L>1, one of the standard representations is L×L matrices over GF(p) so that the arithmetic of GF(pL) can be realized…”
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Circular-Shift-Based Vector Linear Network Coding and Its Application to Array Codes by Jin, Sheng, Zhai, Zhe, Sun, Qifu Tyler, Zhang, Haijun, Li, Zongpeng

“…Circular-shift linear network coding (LNC) is a class of vector LNC with local encoding kernels selected from cyclic permutation matrices, so that it has low…”
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Two-Dimensional Vector Linear Network Coding by Ma, Lan, Sun, Qifu Tyler, Li, Zongpeng

“…In this work, we introduce a new framework of linear network coding (LNC) schemes called two-dimensional (2D) vector LNC, which subsumes conventional (1D)…”
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On Vector Random Linear Network Coding in Wireless Broadcasts by Su, Rina, Zhao, Chengji, Sun, Qifu, Zhang, Zhongshan

“…Compared with scalar linear network coding (LNC) formulated over the finite field GF(2L), vector LNC offers enhanced flexibility in the code design by enabling…”
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A Unified Framework of Array Codes Based on Vector Linear Network Coding by Sun, Qifu Tyler, Jin, Sheng, Zhai, Zhe, Wei, Hao, Li, Zongpeng

“…Inspired by the algebraic framework of vector linear network coding, we advocate in this paper to characterize an L-dimensional (n, k) array code by a k…”
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On the Message Dimensions of Vector Linearly Solvable Networks by Das, Niladri, Rai, Brijesh Kumar

“…It is known that there exists a network which does not have a scalar linear solution over any finite field but has a vector linear solution when message…”
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Characteristic Sets of Fixed-Dimension Vector Linear Codes for Non-Multicast Networks by Das, Niladri, Rai, Brijesh Kumar

“… In this paper, we show the interdependency between the characteristic of the finite field and the dimension of the vector linear network code that achieves a vector linear network coding (VLNC…”
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On the Power of Vector Linear Network Coding by Das, Niladri, Rai, Brijesh Kumar

“…This paper presents yet another instance of the power of vector linear network coding over scalar linear network coding…”
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Circular-shift-based Vector Linear Network Coding and Its Application to Array Codes by Sheng, Jin, Zhai, Zhe, Qifu Tyler Sun, Li, Zongpeng

“…Circular-shift linear network coding (LNC) is a class of vector LNC with local encoding kernels selected from cyclic permutation matrices, so that it has low…”
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Network coding with computation alignment by Goela, N., Changho Suh, Gastpar, M.

“…Determining the capacity of multi-receiver networks with arbitrary message demands is an open problem in the network coding literature. In this paper, we…”
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On Network Coding for Sum-Networks by Rai, Brijesh Kumar, Dey, Bikash Kumar

“…A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a…”
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On the Gap Between Scalar and Vector Solutions of Generalized Combination Networks by Liu, Hedongliang, Wei, Hengjia, Puchinger, Sven, Wachter-Zeh, Antonia, Schwartz, Moshe

“… These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a lower bound and an upper bound on the gap in the alphabet size between optimal scalar-linear and optimal vector-linear network coding solutions…”
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On Vector Linear Solvability of Multicast Networks by Sun, Qifu Tyler, Xiaolong Yang, Keping Long, Xunrui Yin, Zongpeng Li

“…Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an L-dimensional vector of data symbols over a base field GF(q…”
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On Interference Networks Over Finite Fields by Song-Nam Hong, Caire, Giuseppe

“…We present a framework to study linear deterministic interference networks over finite fields. Unlike the popular linear deterministic models introduced to…”
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Vector Linear Solution iff Dimension \geq m by Das, Niladri, Rai, Brijesh Kumar

“…If a network has an <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula>-dimensional vector linear network coding…”
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Vector Linear Solution iff Dimension [Formula Omitted] by Das, Niladri, Rai, Brijesh Kumar

“…If a network has an [Formula Omitted]-dimensional vector linear network coding (VLNC) solution, then it also has a VLNC solution for all dimensions multiple…”
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On vector linear solvability of multicast networks by Qifu Sun, Xiaolong Yangy, Keping Long, Xunrui Yin, Zongpeng Li

“…In the literature of network coding, vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted…”
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On the Gap between Scalar and Vector Solutions of Generalized Combination Networks by Liu, Hedongliang, Hengjia Wei, Puchinger, Sven, Wachter-Zeh, Antonia, Schwartz, Moshe

“… These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a lower bound and an upper bound on the gap in the alphabet size between optimal scalar-linear and optimal vector-linear network coding solutions…”
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On Vector Linear Solvability of Multicast Networks by Qifu Tyler Sun, Yang, Xiaolong, Long, Keping, Yin, Xunrui, Li, Zongpeng

“…Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an \(L…”
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Constructing multicast networks where vector linear coding outperforms scalar linear coding by Sun, Qifu, Yang, Xiaolong, Long, Keping, Li, Zongpeng

“…Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an L-dimensional vector of data symbols over a base field GF(q…”
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