Communication Over Finite-Field Matrix Channels

Silva, D.; Kschischang, Frank R.; Kötter, Ralf

doi:10.1109/tit.2009.2039167

Cited by 64 publications

(129 citation statements)

References 17 publications

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“…In the first case we extend the syndrome decoding method to correct Hamming errors for index codes given in [11] to the ICCSI case. In the second, we show that the simple, low-complexity strategy for additive matrix channels given in [35] can be applied to correct rank-metric errors, that is to handle error matrices of rank upper bounded by some δ.…”

Section: A Our Contributionmentioning

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: A Our Contributionmentioning

confidence: 99%

“…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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confidence: 99%

Error Correction for Index Coding With Coded Side Information

Byrne

Calderini

2017

IEEE Trans. Inform. Theory

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“…The effort of exploiting the network characteristic moves from the network to the transmitter and the receiver, respectively. The idea of linear channel operator (LOC) has been studied by various authors [48,52,53] and has demonstrated to be useful to model a random channel with error control coding properties.…”

Section: Network Error Correctionmentioning

confidence: 99%

A Survey of Linear Network Coding and Network Error Correction Code Constructions and Algorithms

Sanna

Izquierdo

2011

International Journal of Digital Multimedia Broadcasting

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Network coding was introduced by Ahlswede et al. in a pioneering work in 2000. This paradigm encompasses coding and retransmission of messages at the intermediate nodes of the network. In contrast with traditional store-and-forward networking, network coding increases the throughput and the robustness of the transmission. Linear network coding is a practical implementation of this new paradigm covered by several research works that include rate characterization, error-protection coding, and construction of codes. Especially determining the coding characteristics has its importance in providing the premise for an efficient transmission. In this paper, we review the recent breakthroughs in linear network coding for acyclic networks with a survey of code constructions literature. Deterministic construction algorithms and randomized procedures are presented for traditional network coding and for network-control network coding.

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“…To study this, we need to calculate the capacity of noncoherent network coding [21], [22], [24], [25].…”

Section: Removing the Coding Vectors: Noncoherent Network Codingmentioning

confidence: 99%

Network Coding: Beyond Throughput Benefits

Fragouli

2011

Proc. IEEE

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Abstract-Network coding enables novel network functionalities and thus offers a wider canvas of choices when optimizing an information flow problem. In this paper we examine the simplest possible information flow problem, a unicast connection, and explore what we believe is one of the most attractive features network coding offers: the ability to enable near optimal performance in a completely decentralized and randomized setting. This is an especially attractive feature for wireless applications. However, it comes at the cost of an overhead in terms of rate, that can be significant for applications that operate using relatively short frame lengths, as is the case in the wireless setting. We review the efforts in the literature to either alleviate this overhead, or alternatively, to exploit it for network management and control.

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Communication Over Finite-Field Matrix Channels

Cited by 64 publications

References 17 publications

Error Correction for Index Coding With Coded Side Information

Error Correction for Index Coding With Coded Side Information

A Survey of Linear Network Coding and Network Error Correction Code Constructions and Algorithms

Network Coding: Beyond Throughput Benefits

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