On the capacity of sum-networks

Kumar, Brijesh; Das, Niladri

doi:10.1109/allerton.2013.6736711

Cited by 9 publications

(19 citation statements)

References 24 publications

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“…The work of Rai and Das [28] is closest in spirit to our work. In [28], the authors gave a construction procedure to obtain a sum-network with computation capacity equal to p/q, where p, q are any two co-prime natural numbers. The procedure involved first constructing a sum-network whose capacity was 1/q.…”

Section: A Comparison With Prior Workmentioning

confidence: 69%

“…Our work in [29] answered it in the affirmative and proposed a general construction procedure that returned sum-networks with a prescribed computation capacity. The sum-networks in [28] could be obtained as special cases of this construction procedure. Some smaller instances of sum-networks for specific values were presented in [30].…”

Section: Background Related Work and Summary Of Contributionsmentioning

confidence: 99%

“…In [28], the authors also posed the question if smaller sumnetworks (with lesser sources and terminals) with capacity as p/q existed. Using the procedure described in this paper, we can answer that question in the affirmative.…”

Section: A Comparison With Prior Workmentioning

confidence: 99%

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Sum-Networks From Incidence Structures: Construction and Capacity Analysis

Tripathy

Ramamoorthy

2018

IEEE Trans. Inform. Theory

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Abstract-A sum-network is an instance of a function computation problem over a directed acyclic network in which each terminal node wants to compute the sum over a finite field of the information observed at all the source nodes. Many characteristics of the well-studied multiple unicast network communication problem also hold for sum-networks due to a known reduction between the two problems. In this work, we describe an algorithm to construct families of sum-network instances using incidence structures. The computation capacity of several of these sumnetwork families is evaluated. Unlike the coding capacity of a multiple unicast problem, the computation capacity of sumnetworks depends on the characteristic of the finite field over which the sum is computed. This dependence is very strong; we show examples of sum-networks that have a rate-1 solution over one characteristic but a rate close to zero over a different characteristic. Additionally, a sum-network can have arbitrarily different computation capacities for different alphabets.

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Section: A Comparison With Prior Workmentioning

confidence: 69%

Section: Background Related Work and Summary Of Contributionsmentioning

confidence: 99%

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Sum-Networks From Incidence Structures: Construction and Capacity Analysis

Tripathy

Ramamoorthy

2018

IEEE Trans. Inform. Theory

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“…Specifically, [4] constructs sum-networks whose solvability depends on the field characteristic under the restriction of linear network coding. Given a ratio p/q < 1, it was shown in [8] that there exist sum-networks which have p/q as their coding capacity. Reference [9] described a systematic construction procedure for sum-networks with capacity p/q; these are typically smaller than those in [8].…”

Section: Introductionmentioning

confidence: 99%

“…Given a ratio p/q < 1, it was shown in [8] that there exist sum-networks which have p/q as their coding capacity. Reference [9] described a systematic construction procedure for sum-networks with capacity p/q; these are typically smaller than those in [8]. The capacity of these sum-networks however was independent of the message alphabet.…”

Section: Introductionmentioning

confidence: 99%

Capacity of sum-networks for different message alphabets

Tripathy

Ramamoorthy

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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Abstract-A sum-network is a directed acyclic network in which all terminal nodes demand the 'sum' of the independent information observed at the source nodes. Many characteristics of the well-studied multiple-unicast network communication problem also hold for sum-networks due to a known reduction between instances of these two problems. Our main result is that unlike a multiple unicast network, the coding capacity of a sum-network is dependent on the message alphabet. We demonstrate this using a construction procedure and show that the choice of a message alphabet can reduce the coding capacity of a sum-network from 1 to close to 0.

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On characteristics dependent linear coding capacity of sum‐networks

Kumar

Das

2017

IET Networks

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It is known that the linear coding capacity of non-multicast networks may depend on the characteristic of the finite field. Such a dependence has been demonstrated in several examples presented in the literature. However, in all such examples, the number of distinct values that the linear coding capacity can take over different characteristics of the finite field is two. For example, the Fano network has linear coding capacity equal to one over even characteristic, and has linear coding capacity equal to 4/5 over odd characteristics. It is a natural question that whether a network can have arbitrarily many different characteristics dependent linear coding capacities. In this study, the authors answer the question for sum-networks, which are networks where the terminals demand the sum of the messages generated by the sources. Specifically, they show that given a set of characteristics (prime numbers) {p 1 , p 2 , …, p n }, indeed there exists a sum-network such that for each different value of the characteristic of the finite field, the linear coding capacity of the sum-network is different.

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On the capacity of sum-networks

Cited by 9 publications

References 24 publications

Sum-Networks From Incidence Structures: Construction and Capacity Analysis

Sum-Networks From Incidence Structures: Construction and Capacity Analysis

Capacity of sum-networks for different message alphabets

On characteristics dependent linear coding capacity of sum‐networks

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