Linear Index Coding via Semidefinite Programming

Chlamtáč, Eden; Haviv, Ishay

doi:10.1137/1.9781611973099.35

Cited by 12 publications

(5 citation statements)

References 29 publications

(33 reference statements)

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“…Note that the quantity 1 R can be interpreted as the average number of time slots required for all the destinations to get a message from S. In much of the index coding literature, the minimum value of 1 R over the set of all achievable rates -or equivalently, the reciprocal of the symmetric capacity -is the primary object of study and is often denoted as β (e.g. [17,23,24,25,26]). Indeed, in these works, the index coding problem is formulated as one where the goal is to minimize β, which is equivalent to determining the symmetric capacity of the problem.…”

Section: Symmetric Capacitymentioning

confidence: 99%

“…It was recognized in [2,31] that the reciprocal of the symmetric rate achievable by the optimal scalar linear code over field F is equal to the minrank of the side information graph evaluated over F 7 . Algorithms for finding or approximating the minrank function are proposed in [32] and [23]. Haviv and Langberg in [24] investigated the minranks of random digraphs.…”

Section: Insufficiency Of Linear Codes For Multiple Unicast Index Codingmentioning

confidence: 99%

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Index coding: An interference alignment perspective

Maleki

Cadambe

Jafar

2012

2012 IEEE International Symposium on Information Theory Proceedings

124

246

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The index coding problem is studied from an interference alignment perspective providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between the capacity of the multiple unicast index coding (where each message is desired by exactly one receiver), and groupcast index coding (where a message can be desired by multiple receivers), which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings where this question has previously been answered. Necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints, and generalizations to feasibility of rateper message when each destination desires at least L messages, are similarly obtained. Finally, capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks. The solutions are based on vector linear coding. * Presented in part at ISIT 2012. Hamed Maleki and Syed Jafar (email: hmaleki@uci.edu, syed@uci.edu) are with the Center for Pervasive Communications and Computing (CPCC) at

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Section: Symmetric Capacitymentioning

confidence: 99%

Section: Insufficiency Of Linear Codes For Multiple Unicast Index Codingmentioning

confidence: 99%

Index coding: An interference alignment perspective

Maleki

Cadambe

Jafar

2012

2012 IEEE International Symposium on Information Theory Proceedings

124

246

View full text Add to dashboard Cite

show abstract

“…The problem of delay minimization in IDNC for erasure free channels have been studied in the literature under the name of index coding (IC), introduced by Birk and Kol [77] previously and extensively studied in [78,79,80,81,82,83,84,85,86].…”

Section: Motivation Of Instantly Decodable Network Codingmentioning

confidence: 99%

Instantly Decodable Network Coding: From Centralized to Device-to-Device Communications

Douik

Sorour

Al-Naffouri

et al. 2017

IEEE Commun. Surv. Tutorials

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Instantly Decodable Network Coding: From Centralized to Device-to-Device Communications Ahmed DouikFrom its introduction to its quindecennial, network coding has built a strong reputation in enhancing the packet recovery process and achieving maximum information flow in both wired and wireless networks. Traditional studies focused on optimizing the throughput of the network by proposing complex schemes that achieve optimal delay. With the shift toward distributed computing on mobile devices, throughput and complexity become both critical factors that affect the efficiency of a coding scheme. Instantly decodable network coding imposed itself as a new paradigm in network coding that trades off these two aspects. This paper presents a survey of instantly decodable network coding schemes that are proposed in the literature. The various schemes are identified, categorized and evaluated. Two categories can be distinguished namely the conventional centralized schemes and the distributed or cooperative schemes. For each scheme, the comparison is carried out in terms of reliability, performance, complexity and packet selection methodology. Although the performance is generally inversely proportional to the computation complexity, numerous successful schemes from both the performance and complexity viewpoint are identified.

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“…On one hand, people focus on characterising the transmission efficiency performance limit of the IC problem: The work in tries to approximate the broadcast capacity of the IC problem, and the work in identifies the side information graphs whose optimal IC can be found efficiently. On the other hand, in order to be applied into practical systems, some efficient sub‐optimal algorithms based on certain constructed graphs are proposed . There are also works on reducing the computation burden, which consequently reduces energy consumption at transmitters or receivers, represented by the sparse IC problem , and the binary‐IC problem where the finite field size is restricted to be two .…”

Section: Cooperative Strategies For Wireless Relay Channelsmentioning

confidence: 99%

Survey on cooperative strategies for wireless relay channels

Dai

Wang

Zhang

et al. 2014

Trans. Emerging. Tel. Tech.

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Cooperative communication has the potential of providing better throughput and reliability to wireless systems when compared with direct communication. To realise the potential gain, it is important to design cooperative strategies for some representative scenarios. This survey deals with three basic wireless relay channels, namely, the parallel relay channel, the multiple‐access relay channel and the broadcast relay channel. For the first channel, which models a single unicast connection, various forwarding strategies are studied. For the second and third channels, which model, respectively, the uplink and downlink scenarios with multiple unicast connections; network codes that exploit the possibility of coding among the connections are studied. The common aim pertaining to the studies of all these three channels is to use the limited radio resource in the most efficient way. Beside the aforementioned conventional works, studies that have state‐of‐the‐art assumptions for relay networks, including outdated channel state information at the transmitter, full duplex relay and practical rateless‐coded cooperation, are also extensively reviewed. Copyright © 2014 John Wiley & Sons, Ltd.

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Linear Index Coding via Semidefinite Programming

Cited by 12 publications

References 29 publications

Index coding: An interference alignment perspective

Index coding: An interference alignment perspective

Instantly Decodable Network Coding: From Centralized to Device-to-Device Communications

Survey on cooperative strategies for wireless relay channels

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