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...tly. A computable characterization of β is not known in general. Consequently, numerous coding schemes have been proposed in the literature with varying degrees of generality and performance [1]–[8], =-=[14]-=-. Among these, we focus on the coding schemes by Birk and Kol [1], by Blasiak, Kleinberg, and Lubetzky [6] and by Shanmugam, Dimakis, and Langberg [8] that can be viewed 2014 IEEE International Sympos...

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...ental problem attracted several research communities (see [2]–[5] for a subset of recent contributions). The capacity region has been established for all 9,608 index coding problems of n = 5 messages =-=[6]-=- (which includes all index coding problems up to five messages by taking projections). However, the coding schemes developed for small n prove to be suboptimal when n becomes large and there is no kno...

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...ected G, or a planar bipartite graph. Hence existing results [2], [6] do not subsume the result of this paper. In a slightly different setup, a similar result has been obtained by Arbabjolfaei et al. =-=[7]-=-, who derived the optimal code rate for all unicast index-coding instances with up to five receivers. In their setup, each message xi contains BRi bits (for i ∈ {1, . . . , n}), and the sender broadca...

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...emma 2 and Remark 1 in Appendix.) • Second, we further identify certain situations under which (P2) = (P1(Gcl(P2))). • Third, based on the existing symmetric capacity result for C1 with n = m ≤ 5 =-=[4]-=-, (P2) ≥ (P1(Gcl(P2))) [6], and our new result, we compute the symmetric capacity for C2 with n < m ≤ 5. In the case to which the first result in the above applies, the above result simply yields ...

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...8 by Birk and Kol [1] in the context of satellite communication. Since then, it has been studied by researchers in diverse areas using algebraic [2]–[4], graph theoretical [5], [6], and random coding =-=[7]-=- tools. However, none of the proposed inner and outer bounds on the capacity region is tight in general, and the problem of even approximating the capacity region within a factor of O(n1−ǫ) still rema...

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...oring and multiple unicast networks were investigated in [23] and [16], respectively. The work in [24] investigated the property of index codes on random graphs. Tools from network information theory =-=[25]-=-, [26] and distributed source coding [27] were also used to tackle the index coding problem. Related to index coding is the line of work on distributed caching in [28], [29]. Recently, a matrix comple...

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...ounds for general networks, showing the surprising expressiveness of the problem. Second, interference alignment alongside information theoretic approaches have been recently applied for index coding =-=[5]-=-, [6], [9]–[11] introducing new interesting techniques for code constructions. Briefly, index coding is a noiseless broadcast problem where m messages needs to be sent to n users each requesting one o...