A Homomorphism Transform Based Analysis of Sparse Random Linear Network Coding Over Erasure Channels

In this letter, we provide a method for deriving the first exact expression for the decoding success probability of sparse random linear network coding over erasure channels. The key idea of the proposed method is to transform the characterization of the full rank probability of a sparse random matr...

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Bibliographic Details
Published in:IEEE communications letters Vol. 26; no. 9; pp. 2009 - 2013
Main Authors: Chen, Wenlin, Lu, Fang, Dong, Yan
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Additives
Channels
Coding
Decoding
Encoding
Fields (mathematics)
full rank probability
Homomorphisms
Receivers
Reliability
Sparse matrices
Sparse random linear network coding
Transforms
ISSN:1089-7798, 1558-2558
Online Access:Get full text
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Summary:In this letter, we provide a method for deriving the first exact expression for the decoding success probability of sparse random linear network coding over erasure channels. The key idea of the proposed method is to transform the characterization of the full rank probability of a sparse random matrix into the characterization of the homomorphism transform of the sparse distribution and to obtain a closed-form exact expression for the homomorphism transform of the sparse distribution. The former is solved by employing Möbius inversion theorem and the property of the homomorphism transform, and the latter is solved by employing the feature of the sparse distribution and the property of the nontrivial character of a finite field.
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ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2022.3181722