A Lifting Construction for Scalar Linear Index Codes

Bhattaram, Roop Kumar; Vaddi, Mahesh Babu; Rajan, B. Sundar

doi:10.48550/arxiv.1510.08592

Cited by 2 publications

(6 citation statements)

References 6 publications

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“…In [6], we proposed a lifting construction which constructs a sequence of multiple unicast index problems with one-sided antidotes with a scalar linear index code starting from a given multiple unicast index coding problem with a known scalar linear index code. The construction in this paper is different in the following two respects:…”

Section: A Contributionsmentioning

confidence: 99%

“…1) The construction in [6] starts from a problem with K messages and gives a sequence of problems with mK number of messages for m = 2, 3, . .…”

Section: A Contributionsmentioning

confidence: 99%

“…Whereas in this work the number of messages remains K and only the size of the antidote sets increase. 2) In [6] new scalar linear index codes are obtained starting from a scalar linear index code for problems of different source sizes whereas in this paper new vector linear index codes are obtained starting from a scalar linear index code for the problem with the same source size.…”

Section: A Contributionsmentioning

confidence: 99%

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Optimal vector linear index codes for some symmetric side information problems

Vaddi

Rajan

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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The capacity of symmetric instance of the multiple unicast index coding problem with neighboring antidotes (sideinformation) with number of messages equal to the number of receivers was given by Maleki, Cadambe and Jafar in [1]. In this paper we consider ten symmetric multiple unicast problems with lesser antidotes than considered in [1] and explicitly construct scalar linear codes for them. These codes are shown to achieve the capacity or equivalently these codes shown to be of optimal length. Also, the constructed codes enable the receivers use small number of transmissions to decode their wanted messages which is important to have the probability of message error reduced in a noisy broadcast channel [8], [10]. Some of the cases considered are shown to be critical index coding problems and these codes help to identify some of the subclasses considered in [1] to be not critical index coding problems. 1 min(U,D)+1 K+min(U,D)−max(U,D)

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Section: A Contributionsmentioning

confidence: 99%

“…1) The construction in [6] starts from a problem with K messages and gives a sequence of problems with mK number of messages for m = 2, 3, . .…”

Section: A Contributionsmentioning

confidence: 99%

Section: A Contributionsmentioning

confidence: 99%

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Optimal vector linear index codes for some symmetric side information problems

Vaddi

Rajan

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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“…Characterisation of the optimal codelengths of SUICPs in terms of those of its sub-problems has been carried out in many works [5], [11]- [15]. A lifting construction was presented in [11], where a special class of SUICPs were obtained from another class of SUICPs. The optimal scalar linear codelength of the larger derived SUICP has been shown to be equal to that of the smaller SUICP.…”

Section: Introductionmentioning

confidence: 99%

“…Graph homomorphism between complements of the side-information digraphs of two given SUICPs was used to establish a relation between their optimal codelengths [12]. Some special classes of rank invariant extensions of any SUICP were presented in [13], where the extended problems have the same optimal linear codelength as that of the original SUICP, generalizing the results of [11]. The notion of rank invariant extensions was extended to a class of joint extensions of any finite number of SUICPs in [14].…”

Section: Introductionmentioning

confidence: 99%

Groupcast Index Coding Problem: Joint Extensions

Arunachala,

Rajan

2018

Preprint

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The groupcast index coding problem is the most general version of the classical index coding problem, where any receiver can demand messages that are also demanded by other receivers. Any groupcast index coding problem is described by its fitting matrix which contains unknown entries along with 1's and 0's. The problem of finding an optimal scalar linear code is equivalent to completing this matrix with known entries such that the rank of the resulting matrix is minimized. Any row basis of such a completion gives an optimal scalar linear code. An index coding problem is said to be a joint extension of a finite number of index coding problems, if the fitting matrices of these problems are disjoint submatrices of the fitting matrix of the jointly extended problem. In this paper, a class of joint extensions of any finite number of groupcast index coding problems is identified, where the relation between the fitting matrices of the sub-problems present in the fitting matrix of the jointly extended problem is defined by a base problem. A lower bound on the minrank (optimal scalar linear codelength) of the jointly extended problem is given in terms of those of the subproblems. This lower bound also has a dependence on the base problem and is operationally useful in finding lower bounds of the jointly extended problems when the minranks of all the subproblems are known. We provide an algorithm to construct scalar linear codes (not optimal in general), for any groupcast problem belonging to the class of jointly extended problems identified in this paper. The algorithm uses scalar linear codes of all the subproblems and the base problem. We also identify some subclasses, where the constructed codes are scalar linear optimal.

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A Lifting Construction for Scalar Linear Index Codes

Cited by 2 publications

References 6 publications

Optimal vector linear index codes for some symmetric side information problems

Optimal vector linear index codes for some symmetric side information problems

Groupcast Index Coding Problem: Joint Extensions

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