On the Minimum Number of Transmissions in Single-Hop Wireless Coding Networks

Rouayheb, Salim Y. El; Chaudhry, Mohammad Asad Rehman; Sprintson, Alex

doi:10.1109/itw.2007.4313060

Cited by 120 publications

(131 citation statements)

References 3 publications

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“…We need to find an illustration of the possible message combinations, those are decodable at the same instant by all the users or any subset of them. In [34,35,36] …”

Section: Idnc Graphmentioning

confidence: 99%

Rate aware network codes for coordinated multi base-station networks

Saif

Douik

Sorour

2016

2016 IEEE International Conference on Communications (ICC)

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“…We need to find an illustration of the possible message combinations, those are decodable at the same instant by all the users or any subset of them. In [34,35,36] …”

Section: Idnc Graphmentioning

confidence: 99%

Rate aware network codes for coordinated multi base-station networks

Saif

Douik

Sorour

2016

2016 IEEE International Conference on Communications (ICC)

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“…The matrix F BC is as in (13) and B matrix is as in (14). There are three linear codes which are optimal in terms of length.…”

Section: Partitioning Of Matrix Bmentioning

confidence: 99%

On the number of optimal linear index codes for unicast index coding problems

Kavitha¹,

Ambadi²,

Rajan³

2016

2016 IEEE Wireless Communications and Networking Conference

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Abstract-An index coding problem arises when there is a single source with a number of messages and multiple receivers each wanting a subset of messages and knowing a different set of messages a priori. The noiseless Index Coding Problem is to identify the minimum number of transmissions (optimal length) to be made by the source through noiseless channels so that all receivers can decode their wanted messages using the transmitted symbols and their respective prior information. Recently [8], it is shown that different optimal length codes perform differently in a noisy channel. Towards identifying the best optimal length index code one needs to know the number of optimal length index codes. In this paper we present results on the number of optimal length index codes making use of the representation of an index coding problem by an equivalent network code. Our formulation results in matrices of smaller sizes compared to the approach of Kotter and Medard [6]. Our formulation leads to a lower bound on the minimum number of optimal length codes possible for all unicast index coding problems [1] which is met with equality for several special cases of the unicast index coding problem. A method to identify the optimal length codes which lead to minimum-maximum probability of error is also presented.

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“…By the equivalence of the universal recovery problem on a network T to the network coding problem on G N C T and the max-flow min-cut theorem for network information flow, if a transmission scheme permits universal recovery in T , then the associated b j i 's must satisfy the constraints of the form given by (8). Conversely, for any set of b j i 's which satisfy the constraints of the form given by (8), there exists a transmission scheme using exactly those numbers of transmissions which permits universal recovery.…”

Section: Appendixmentioning

confidence: 99%

Efficient universal recovery in broadcast networks

Courtade

Wesel

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-Consider a connected broadcast network of N nodes that all wish to recover k desired packets. Each node begins with a subset of the desired packets and broadcasts messages to its neighbors. In a previous paper we established necessary and sufficient conditions on the number of transmissions from each node required for universal recovery (in which each node recovers all k packets). However, these conditions are numerous and cumbersome. The present paper gives a series of relatively simple conditions for universal recovery that apply when the number of packets is large and the distribution of packets among the nodes is well behaved.Our first result, which applies to any fixed network topology, uses only simple cuts in the network to characterize a set of transmission strategies such that for any > 0 these strategies require at most k transmissions above the minimum required for universal recovery. For certain topologies including nonsingular d-regular d-connected networks, we explicitly construct transmission strategies that achieve universal recovery while using at most N transmissions above the minimum even when the total number of required transmissions is very large. These explicit constructions essentially resolve the problem completely for many canonical networks (e.g. cliques, rings, grids on tori, etc.).

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On the Minimum Number of Transmissions in Single-Hop Wireless Coding Networks

Cited by 120 publications

References 3 publications

Rate aware network codes for coordinated multi base-station networks

Rate aware network codes for coordinated multi base-station networks

On the number of optimal linear index codes for unicast index coding problems

Efficient universal recovery in broadcast networks

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