On the Gap between Scalar and Vector Solutions of Generalized Combination Networks

Liu, Hedongliang; Wei, Hengjia; Puchinger, Sven; Wachter-Zeh, Antonia; Schwartz, Moshe

doi:10.1109/isit44484.2020.9173942

Cited by 1 publication

(4 citation statements)

References 17 publications

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“…It would be of interest to narrow the gap by new methods. Bq(n, k, δ; α) 1 ≤ δ ≤ k (α − 1)q (k−δ+1)(n−k) [17] Ω(q…”

Section: Discussionmentioning

confidence: 99%

“…The upper bounds on the size of covering Grassmannian codes have been investigated with different objects, such as generalized combination network [10,17], subspace packing [8] and independent configuration [4]. For convenience, we restate the known upper bounds via the notation of covering Grassmannian codes.…”

Section: Preliminariesmentioning

confidence: 99%

“…In [17], Liu et al improved the theorem above by removing some conditions and got the following result.…”

Section: Theorem Ii4 ([8]mentioning

confidence: 99%

“…They also proved that optimal covering Grassmannian codes have minimal requirements for network coding solutions of some generalized combination networks. This family of networks was used in [9] and [17] to show that vector network coding outperforms scalar linear network coding on multicast networks. An α-(n, k, δ) c q covering Grassmannian code C (α-(n, k, δ) c q code for short) consists of a set of k-subspaces of F n q such that every set of α codewords spans a subspace of dimension at least k + δ.…”

Section: Introductionmentioning

confidence: 99%

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Covering Grassmannian Codes: Bounds and Constructions

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et al. 2022

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Grassmannian Gq(n, k) is the set of all k-dimensional subspaces of the vector space F n q . Recently, Etzion and Zhang introduced a new notion called covering Grassmannian code which can be used in network coding solutions for generalized combination networks. An α-(n, k, δ) c q covering Grassmannian code C is a subset of Gq(n, k) such that every set of α codewords of C spans a subspace of dimension at least δ + k in F n q . In this paper, we derive new upper and lower bounds on the size of covering Grassmannian codes. These bounds improve and extend the parameter range of known bounds.

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“…It would be of interest to narrow the gap by new methods. Bq(n, k, δ; α) 1 ≤ δ ≤ k (α − 1)q (k−δ+1)(n−k) [17] Ω(q…”

Section: Discussionmentioning

confidence: 99%