On the capacity region for index coding

Arbabjolfaei, Fatemeh; Bandemer, Bernd; Kim, Young-Han; Şaşoğlu, Eren; Wang, Lele

doi:10.1109/isit.2013.6620369

Cited by 146 publications

(223 citation statements)

References 21 publications

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“…By setting the rate for each receiver the same, their capacity region result yields the symmetric capacity, which is the inverse of the optimal broadcast rate β defined in Definition 4. The obtained symmetric capacity result in the case of n = m ≤ 5 in [4] can be used to obtain the symmetric capacity in the case of n < m ≤ 5, based on Theorem 1 and the result (P 2 ) ≥ (P 1 (G cl (P 2 ))) by Lubetzky and Stav [6]. There exist 9846 non-isomorphic C 1 -index coding problems with n = m ≤ 5 [4].…”

Section: Ieee International Symposium On Information Theorymentioning

confidence: 96%

“…However, in [6], Lubetzky and Stav showed that there exist certain cases in which nonlinear index coding strictly outperforms linear index coding. In [4], Arbabjolfaei et al obtained the capacity region for index coding with up to five receivers for C 1 . By using this result and setting all user rates the same, one can obtain the symmetric capacity for C 1 with up to five receivers.…”

Section: A Related Workmentioning

confidence: 99%

“…This implies that M (P 1 (G cl (I EX ))) has * in the positions (2, 1), (2,4) and (2, 5) in (2). Since N (3) = {2}, receiver r 3 does not know…”

Section: B Backgroundmentioning

confidence: 99%

“…This implies that 2014 IEEE International Symposium on Information Theory M (P 1 (G cl (I EX ))) has 0 in the positions (3, 1), (3,4) and (3,5) and has * in the position (3,2). Similarly, we can incorporate N (1), N (4) and N (5).…”

Section: B Backgroundmentioning

confidence: 99%

“…In [4], the capacity region of any index coding problem with n = m ≤ 5 is obtained. By setting the rate for each receiver the same, their capacity region result yields the symmetric capacity, which is the inverse of the optimal broadcast rate β defined in Definition 4.…”

Section: Ieee International Symposium On Information Theorymentioning

confidence: 99%

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Some new results on index coding when the number of data is less than the number of receivers

Kwak

Sung

2014

2014 IEEE International Symposium on Information Theory

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Abstract-In this paper, index coding problems in which the number (m) of receivers is larger than that (n) of data are considered. Unlike the case that the two numbers are same (n = m), index coding problems with n ≤ m are more general and hard to handle. To circumvent this difficulty, problems with n < m are approached via corresponding problems with n = m. It is shown that in certain cases, the symmetric capacity and code construction for index coding problems with n < m can be obtained from the existing symmetric capacity result and codes for index coding problems with n = m. Such cases include cases with n < m ≤ 5.

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Section: Ieee International Symposium On Information Theorymentioning

confidence: 96%

Section: A Related Workmentioning

confidence: 99%

“…This implies that M (P 1 (G cl (I EX ))) has * in the positions (2, 1), (2,4) and (2, 5) in (2). Since N (3) = {2}, receiver r 3 does not know…”

Section: B Backgroundmentioning

confidence: 99%

Section: B Backgroundmentioning

confidence: 99%

Section: Ieee International Symposium On Information Theorymentioning

confidence: 99%

See 3 more Smart Citations

Some new results on index coding when the number of data is less than the number of receivers

Kwak

Sung

2014

2014 IEEE International Symposium on Information Theory

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Code Equivalences Between Network Codes With Link Errors and Index Codes With Side Information Errors

Kim

2019

IEEE Access

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In this paper, new equivalence relationships between a network code with link errors (NCLE) and an index code with side information errors (ICSIE) are studied. First, for a given network coding instance, the equivalent index coding instance is derived, where an NCLE is converted to the corresponding ICSIE and vice versa. Next, for a given index coding instance, the equivalent network coding instance is also derived, where an ICSIE is converted to the corresponding NCLE and vice versa if a pair of encoding functions of an original link and the duplicated link are functionally related in the network code. Finally, several properties of an NCLE are derived from those of the equivalent ICSIE using the fact that the NCLE and the ICSIE are equivalent.

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Multiuser broadcast erasure channel with feedback and side information, and related index coding results

Παπαδόπουλος

Georgiadis

2014

2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We consider the N-user broadcast erasure channel with public feedback and side information. Before the beginning of transmission, each receiver knows a function of the messages of some of the other receivers. This situation arises naturally in wireless and in particular cognitive networks where a node may overhear transmitted messages destined to other nodes before transmission over a given broadcast channel begins. We provide an upper bound to the capacity region of this system. Furthermore, when the side information is linear, we show that the bound is tight for the case of two-user broadcast channels. The special case where each user knows the whole or nothing of the message of each other node, constitutes a generalization of the index coding problem. For this instance, and when there are no channel errors, we show that the bound reduces to the known Maximum Weighted Acyclic Induced Subgraph bound. We also show how to convert the capacity upper bound to transmission completion rate (broadcast rate) lower bound and provide examples of codes for certain information graphs for which the bound is either achieved of closely approximated.

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On the capacity region for index coding

Cited by 146 publications

References 21 publications

Some new results on index coding when the number of data is less than the number of receivers

Some new results on index coding when the number of data is less than the number of receivers

Code Equivalences Between Network Codes With Link Errors and Index Codes With Side Information Errors

Multiuser broadcast erasure channel with feedback and side information, and related index coding results

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