Bipartite index coding

Tehrani, Arash Saber; Dimakis, Alexandros G.; Neely, Michael J.

doi:10.1109/isit.2012.6283853

Cited by 77 publications

(97 citation statements)

References 12 publications

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“…Note that if for some i, LV (S) Z is non-zero for any Z ∈ Y (i) , then it satisfies the decoding criterion for any possible request vector R i ∈ X (S) , and hence delivers all possible requests to User i. Therefore, Theorem III.12 and Corollary III.13 should be viewed in the context of similar results in [6], [37], which lead to partial clique-cover and partition multicast schemes. There is also a close association with the so-called Main Network Coding Theorem [19, Theorem 2.2] for multicast network coding.…”

Section: Upper Bounds On the Optimal Length Of An F Q -Linear I-icmentioning

confidence: 88%

“…16. The approach in [6] to construct a linear IC for a partial clique is based on maximum distance separable (MDS) codes (this can be used also in the more general case of a multicast group, as described in [37]). Any generator matrix of an MDS linear code of length n and dimension k is such that any k columns are linear independent.…”

Section: Upper Bounds On the Optimal Length Of An F Q -Linear I-icmentioning

confidence: 99%

“…As this number is hard to compute, bounds approximating it are sought, as are algorithms to compute efficient index codes. [37], often taking a graph-theoretic approach. Two interesting generalizations of the problem that have appeared in the literature are the subject of this work.…”

Section: Introductionmentioning

confidence: 99%

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Error Correction for Index Coding With Coded Side Information

Byrne

Calderini

2017

IEEE Trans. Inform. Theory

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Index coding is a source coding problem in which a broadcaster seeks to meet the different demands of several users, each of whom is assumed to have some prior information on the data held by the sender. A well-known application is to satellite communications, as described in one of the earliest papers on the subject [6]. It is readily seen that if the sender has knowledge of its clients' requests and their side-information sets, then the number of packet transmissions required to satisfy all users' demands can be greatly reduced if the data is encoded before sending. The collection of side-information indices as well as the indices of the requested data is described as an instance I of the index coding with side-information (ICSI) problem. The encoding function is called the index code of I, and the number of transmissions employed by the code is referred to as its length. The main ICSI problem is to determine the optimal length of an index code for and instance I. As this number is hard to compute, bounds approximating it are sought, as are algorithms to compute efficient index codes. [37], often taking a graph-theoretic approach. Two interesting generalizations of the problem that have appeared in the literature are the subject of this work. The first of these is the case of index coding with coded side information [10], [34], in which linear combinations of the source data are both requested by and held as users' side-information. This generalization has applications, for example, to relay channels and necessitates algebraic rather than combinatorial methods. The second is the introduction of error-correction in the problem, in which the broadcast channel is subject to noise [11]. In this paper we characterize the optimal length of a scalar or vector linear index code with coded side information (ICCSI) over a finite field in terms of a generalized min-rank and give bounds on this number based on constructions of random codes for an arbitrary instance. We furthermore consider the length of an optimal δ-error correcting code for an instance of the ICCSI problem and obtain bounds analogous to those described in [11], both for the Hamming metric and for rank-metric errors. We describe decoding algorithms for both categories of errors based on those given in [11], [35].

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Section: Upper Bounds On the Optimal Length Of An F Q -Linear I-icmentioning

confidence: 88%

Section: Upper Bounds On the Optimal Length Of An F Q -Linear I-icmentioning

confidence: 99%

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Error Correction for Index Coding With Coded Side Information

Byrne

Calderini

2017

IEEE Trans. Inform. Theory

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“…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. In [7], the authors considered the case of C 2 and showed that a bipartite graph can be used to represent a P 2 .…”

Section: A Related Workmentioning

confidence: 99%

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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“…In order to overcome this problem, efficient alternatives to ARQ protocols for multicast and broadcast were proposed in [2]- [4], based on the idea of erasure recovery. Furthermore, network coding [5] and index coding [6] concepts opened the door for several other algorithms, like the ones considered in [7]- [9]. Another set of methods, based on fountain codes [10]- [12], were introduced.…”

Section: Introductionmentioning

confidence: 99%

Instantly decodable network coding protocols with unequal error protection

Muhammad

Berioli

Liva

et al. 2013

2013 IEEE International Conference on Communications (ICC)

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Abstract-This work aims at introducing two novel packet retransmission techniques for reliable multicast in the framework of Instantly Decodable Network Coding (IDNC). These methods are suitable for order-and delay-sensitive applications, where some information is of high importance for an earlier gain at the receiver's side. We introduce hence an Unequal Error Protection (UEP) scheme, showing by simulations that the Quality of Experience (QoE) for the end-users is improved even without complex encoding and decoding.

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Bipartite index coding

Cited by 77 publications

References 12 publications

Error Correction for Index Coding With Coded Side Information

Error Correction for Index Coding With Coded Side Information

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

Instantly decodable network coding protocols with unequal error protection

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