Coding on demand by an informed source (ISCOD) for efficient broadcast of different supplemental data to caching clients

Birk, Yitzhak; Kol, Tomer

doi:10.1109/tit.2006.874540

Cited by 302 publications

(390 citation statements)

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“…Here, each receiver r i requires X[f (i)] := {x j |j ∈ f (i)}, where f (i) ⊂ [n] := {1, · · · , n} is the index set of the required data for receiver i, and has side information X[N (i)] := {x j |j ∈ N (i)}, where N (i) ⊂ [n] is the index set for the side information for receiver i. The function E(X, {N (·)}) : (0, 1) n → (0, 1) l is an index code of length l if E(X, {N (·)}) is decodable in the Mostly, the index coding problem has been considered in the case in which n = m and f (1), · · · , f(m) is a partition of [n] with |f (i)| = 1, ∀ i [1], [3]- [5]. (We refer to this case as C 1 .)…”

Section: Definitionmentioning

confidence: 99%

“…However, one needs to handle general cases with n = m to accommodate various system setup. An index coding problem in the case of n > m and f (i) ∩ f (j) = ∅ for i = j can trivially be converted to a corresponding problem in the case of n = m and |f (i)| = 1, ∀ i by adding virtual receivers and properly assigning side information for the virtual receivers [1]. However, the case of n < m is not as simple as the case of n > m. (We refer to the case of n < m and |f (i)| = 1 , ∀i as C 2 .…”

Section: Definitionmentioning

confidence: 99%

“…Here, G cl (P 2 ) is a directed graph properly constructed from P 2 as in [6], and P 1 (G) is the C 1 -index coding problem equivalent to a directed graph G. (See [1] for the equivalence between G and P 1 (G).) (·) is the minimum index code length of the corresponding problem.…”

Section: Definitionmentioning

confidence: 99%

“…In [1], the authors showed that considering the case of a single requested data symbol per a receiver is enough, which means considering the case of n ≤ m and |f (i)| = 1, ∀ i is enough, by adding virtual receivers and properly assigning side information for the virtual receivers. In [3], the authors considered the scalar linear index coding for C 1 , and showed that in this case, a P 1 can be represented by a directed graph G(V, E) and the optimal index code length of P 1 is given by a graph parameter of G(V, E).…”

Section: A Related Workmentioning

confidence: 99%

“…Recently, the source coding problem with a broadcast channel with multiple receivers that have side information has drawn much attention from the research community since the problem, named Informed Source Coding On Demand (ISCOD), was first introduced by Birk and Kol [1]. In ISCOD, a transmitter wants to deliver data to receivers by using a broadcast channel with minimum required transmission time, under the assumption that each receiver requires a part of the data and has some side information about the data, and the transmitter knows what side information each receiver has.…”

Section: Introductionmentioning

confidence: 99%

See 4 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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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: Definitionmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: A Related Workmentioning

confidence: 99%

Section: Introductionmentioning

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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Profit‐based exclusive‐or coding algorithm for data retransmission in DVB‐H with a recovery network

Wang

2014

Int J Communication

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SUMMARYThe digital video broadcasting-handheld (DVB-H) standard is developed by European Telecommunications Standards Institute to broadcast digital videos to handheld devices, but data loss is a critical issue due to the broadcast behavior. On the other hand, DVB-Internet protocol datacasting (DVB-IPDC) integrates DVB-H with an Internet protocol-based wireless network to provide bidirectional communication. We adopt this wireless network to deal with data retransmission and call it a recovery network. The paper argues that network coding can improve retransmission efficiency of the recovery network because DVB-H packet loss often exhibits high correlation. In addition, DVB-H packets may be heterogeneous in the sense that they have different importance. According to these two arguments, the paper considers that DVB-H packets are associated with different profit depending on their importance and proposes an˛-maximum profit network coding problem. It asks the base station in the recovery network to use no more than˛coded packets for handheld devices to retrieve the lost DVB-H packets such that the overall profit is the maximum. An efficient exclusive-or coding scheme, namely the profit-based exclusive-or network coding (PEN) algorithm, is proposed to solve this problem. Extensive simulation results also verify the effectiveness of the PEN algorithm.

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Local orthogonality dimension

Inon

Haviv

2023

Journal of Graph Theory

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An orthogonal representation of a graph over a field is an assignment of a vector to every vertex of , such that for every vertex and whenever and are adjacent in . The locality of the orthogonal representation is the largest dimension of a subspace spanned by the vectors associated with a closed neighborhood in the graph. We introduce a novel graph parameter, called the local orthogonality dimension, defined for a given graph and a given field , as the smallest possible locality of an orthogonal representation of over . This is a local variant of the well‐studied orthogonality dimension of graphs, introduced by Lovász, analogously to the local variant of the chromatic number introduced by Erdös et al. We investigate the usefulness of topological methods for proving lower bounds on the local orthogonality dimension. Such methods are known to imply tight lower bounds on the chromatic number of several graph families of interest, such as Kneser graphs and Schrijver graphs. We prove that graphs for which topological methods imply a lower bound of on their chromatic number have local orthogonality dimension at least over every field, strengthening a result of Simonyi and Tardos on the local chromatic number. We show that for certain graphs this lower bound is tight, whereas for others, the local orthogonality dimension over the reals is equal to the chromatic number. More generally, we prove that for every complement of a line graph, the local orthogonality dimension over coincides with the chromatic number. This strengthens a recent result by Daneshpajouh, Meunier, and Mizrahi, who proved that the local and standard chromatic numbers of these graphs are equal. As another extension of their result, we prove that the local and standard chromatic numbers are equal for some additional graphs, from the family of Kneser graphs. We also study the computational aspects of the local orthogonality dimension and show that for every integer and a field , it is NP‐hard to decide whether the local orthogonality dimension of an input graph over is at most . We finally present an application of the local orthogonality dimension to the index coding problem from information theory, extending a result of Shanmugam, Dimakis, and Langberg.

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Coding on demand by an informed source (ISCOD) for efficient broadcast of different supplemental data to caching clients

Cited by 302 publications

References 9 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

Profit‐based exclusive‐or coding algorithm for data retransmission in DVB‐H with a recovery network

Local orthogonality dimension

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