Quasi-linear network coding

Schwartz, Moshe; Médard, Muriel

doi:10.1109/netcod.2014.6892126

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…Related to index coding is the line of work on distributed caching in [28], [29]. Recently, a matrix completion method for constructing linear index codes over finite fields was proposed in [30], and a method for constructing quasilinear vector network codes over the reals was described in [31].…”

Section: Introductionmentioning

confidence: 99%

Index coding and network coding via rank minimization

Huang

Rouayheb

2015

2015 IEEE Information Theory Workshop - Fall (ITW)

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Index codes reduce the number of bits broadcast by a wireless transmitter to a number of receivers with different demands and with side information. It is known that the problem of finding optimal linear index codes is NP-hard. We investigate the performance of different heuristics based on rank minimization and matrix completion methods, such as alternating projections and alternating minimization, for constructing linear index codes over the reals. As a summary of our results, the alternating projections method gives the best results in terms of minimizing the number of broadcast bits and convergence rate and leads to up to 13% savings in average communication cost compared to graph coloring algorithms studied in the literature. Moreover, we describe how the proposed methods can be used to construct linear network codes for non-multicast networks. Our computer code is available online.

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Section: Introductionmentioning

confidence: 99%

Index coding and network coding via rank minimization

Huang

Rouayheb

2015

2015 IEEE Information Theory Workshop - Fall (ITW)

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“…Thus, one can construct an optimal network code by constructing an optimal index code for the equivalent problem. Network codes over real field are discussed in [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Subspace-Aware Index Codes

Kailkhura

Theagarajan

Varshney

2017

IEEE Wireless Commun. Lett.

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In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications (e.g., multimedia), the data to be transmitted may lie (or can be well approximated) in a low-dimensional subspace. We exploit this low-dimensional structure of the data using an algebraic framework to solve the index coding problem (referred to as subspace-aware index coding) as opposed to the traditional index coding problem which is subspace-unaware. Also, we propose an efficient algorithm based on the alternating minimization approach to obtain near optimal index codes for both subspace-aware and -unaware cases.Our simulations indicate that under certain conditions, a significant throughput gain (about 90%) can be achieved by subspace-aware index codes over conventional subspace-unaware index codes.

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On Duplication-Free Codes for Disjoint or Equal-Length Errors

Yu,

Schwartz

2024

Preprint

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Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-duplication errors, and equal-length tandem-duplication errors. We construct codes, with positive asymptotic rate, for the two settings, as well as for their combination. Our constructions are duplication-free codes, comprising codewords that do not contain tandem duplications of specific lengths. Additionally, our codes generalize previous constructions, containing them as special cases. MSC Classification: 68R15 , 94B25 , 94B35

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Quasi-linear network coding

Cited by 3 publications

References 13 publications

Index coding and network coding via rank minimization

Index coding and network coding via rank minimization

Subspace-Aware Index Codes

On Duplication-Free Codes for Disjoint or Equal-Length Errors

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