Network routing capacity

Cannons, J.; Dougherty, Randall; Freiling, Chris; Zeger, K.

doi:10.1109/tit.2005.864474

Cited by 78 publications

(118 citation statements)

References 11 publications

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“…where γ t,i is defined in (2). By choosing the real coefficients α e→e ′ and β t,i , the goal is to minimize F .…”

Section: T)mentioning

confidence: 99%

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Quasi-linear network coding

Schwartz

Médard

2014

2014 International Symposium on Network Coding (NetCod)

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Abstract-We present a heuristic for designing vector nonlinear network codes for non-multicast networks, which we call quasi-linear network codes. The method presented has two phases: finding an approximate linear network code over the reals, and then quantizing it to a vector non-linear network code using a fixed-point representation. Apart from describing the method, we draw some links between some network parameters and the rate of the resulting code.

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“…where γ t,i is defined in (2). By choosing the real coefficients α e→e ′ and β t,i , the goal is to minimize F .…”

Section: T)mentioning

confidence: 99%

“…We can apply the quasi-linear network-coding scheme to this network, and since the two sub-networks operate separately, get a solution with rate 7/20 > 1/3. We can compare this with the best routing solution for this network which has a lower rate of 1/3 (see [2]). …”

Section: Theoremmentioning

confidence: 99%

Quasi-linear network coding

Schwartz

Médard

2014

2014 International Symposium on Network Coding (NetCod)

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“…However, more guarantees can be obtained once we operate a subset of the sinks below their best-case capacity (d i < c i ). This concept of achieving more by relaxing the strict capacity requirement has already appeared in the network coding literature, and was found significantly useful [7], [8]. Here the idea is that with three or more partial demand sinks, for some sink we may exhaust the ways of zeroing columns using non-contaminating column operations.…”

Section: B More Than Two Partial Demand Sinksmentioning

confidence: 99%

Network coding for non-uniform demands

Cassuto

Bruck

2005

Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.

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In this paper we define nonuniform-demand networks as a useful connection model, in between multicasts and general connections. In these networks, the source has a pool of messages, and each sink demands a certain number of messages, without specifying their identities. We study the solvability of such networks and give a tight bound on the number of sinks that achieve capacity in a worst-case network. We propose constructions to solve networks at, or slightly below capacity, and investigate the effect large alphabets have on the solvability of such networks. We also show that our efficient constructions are suboptimal when used in networks with more sinks, yet this comes with little surprise considering the fact that the general problem is shown to be NP-hard.

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“…Vector network coding as part of fractional network coding was mentioned in [2]. A solution of the network is called an (s, t) fractional vector network coding solution, if the edges transmit vectors of length t, but the message vectors are of length s ≤ t. The case s = t = 1 corresponds to a scalar solution.…”

Section: Introductionmentioning

confidence: 99%

Vector network coding based on subspace codes outperforms scalar linear network coding

Etzion

Wachter-Zeh

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Abstract-This paper considers vector network coding solutions based on rank-metric codes and subspace codes. The main result of this paper is that vector solutions can significantly reduce the required alphabet size compared to the optimal scalar linear solution for the same multicast network. The multicast networks considered in this paper have one source with h messages, and the vector solution is over a field of size q with vectors of length t. For a given network, let the smallest field size for which the network has a scalar linear solution be qs, then the gap in the alphabet size between the vector solution and the scalar linear solution is defined to be qs −q t . In this contribution, the achieved gap is q (h−2)t 2 /h+o(t) for any q ≥ 2 and any even h ≥ 4. If h ≥ 5 is odd, then the achieved gap of the alphabet size is q (h−3)t 2 /(h−1)+o(t) . Previously, only a gap of size size one had been shown for networks with a very large number of messages. These results imply the same gap of the alphabet size between the optimal scalar linear and some scalar nonlinear network coding solution for multicast networks. For three messages, we also show an advantage of vector network coding, while for two messages the problem remains open. Several networks are considered, all of them are generalizations and modifications of the well-known combination networks. The vector network codes that are used as solutions for those networks are based on subspace codes, particularly subspace codes obtained from rank-metric codes. Some of these codes form a new family of subspace codes, which poses a new research problem.

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Network routing capacity

Cited by 78 publications

References 11 publications

Quasi-linear network coding

Quasi-linear network coding

Network coding for non-uniform demands

Vector network coding based on subspace codes outperforms scalar linear network coding

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