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Linear Network Error Correction Coding

  • Xuan Guang
  • Zhen Zhang

Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Xuan Guang, Zhen Zhang
    Pages 1-15
  3. Xuan Guang, Zhen Zhang
    Pages 17-31
  4. Xuan Guang, Zhen Zhang
    Pages 51-83
  5. Xuan Guang, Zhen Zhang
    Pages 85-94
  6. Xuan Guang, Zhen Zhang
    Pages 95-103
  7. Back Matter
    Pages 105-107

About this book

Introduction

There are two main approaches in the theory of network error correction coding. In this SpringerBrief, the authors summarize some of the most important contributions following the classic approach, which represents messages by sequences similar to algebraic coding, and also briefly discuss the main results following the other approach, that uses the theory of rank metric codes for network error correction of representing messages by subspaces. This book starts by establishing the basic linear network error correction (LNEC) model and then characterizes two equivalent descriptions. Distances and weights are defined in order to characterize the discrepancy of these two vectors and to measure the seriousness of errors. Similar to classical error-correcting codes, the authors also apply the minimum distance decoding principle to LNEC codes at each sink node, but use distinct distances. For this decoding principle, it is shown that the minimum distance of a LNEC code at each sink node can fully characterize its error-detecting, error-correcting and erasure-error-correcting capabilities with respect to the sink node. In addition, some important and useful coding bounds in classical coding theory are generalized to linear network error correction coding, including the Hamming bound, the Gilbert-Varshamov bound and the Singleton bound. Several constructive algorithms of LNEC codes are presented, particularly for LNEC MDS codes, along with an analysis of their performance. Random linear network error correction coding is feasible for noncoherent networks with errors. Its performance is investigated by estimating upper bounds on some failure probabilities by analyzing the information transmission and error correction. Finally, the basic theory of subspace codes is introduced including the encoding and decoding principle as well as the channel model, the bounds on subspace codes, code construction and decoding algorithms.

Keywords

Attacks from malicious nodes decoding algorithms erasures error correction capability maximum distance separable code minimum distance network coding network error rank metric code singleton bound subspace code

Authors and affiliations

  • Xuan Guang
    • 1
  • Zhen Zhang
    • 2
  1. 1.Department of Information and Probabilit School of Mathematical SciencesNankai UniversityTianjinChina
  2. 2.Ming Hsieh Department of Electrical Engi Viterbi School of EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-0588-1
  • Copyright Information The Author(s) 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Computer Science
  • Print ISBN 978-1-4939-0587-4
  • Online ISBN 978-1-4939-0588-1
  • Series Print ISSN 2191-5768
  • Series Online ISSN 2191-5776
  • Buy this book on publisher's site