The Rank Distribution of Sparse Random Linear Network Coding

Sparse random linear network coding (SRLNC) is a promising solution for reducing the complexity of random linear network coding (RLNC). RLNC can be modeled as a linear operator channel (LOC). It is well known that the normalized channel capacity of LOC is characterized by the rank distribution of th...

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Bibliographic Details
Published in:IEEE access Vol. 7; pp. 43806 - 43819
Main Authors: Chen, Wenlin, Lu, Fang, Dong, Yan
Format: Journal Article
Language:English
Published: Piscataway IEEE 2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximation
Channel capacity
Coding
Complexity theory
Decoding
Encoding
Fields (mathematics)
Linear operators
Mathematical analysis
Network coding
Operators (mathematics)
Probability
Rank distribution
Sparse matrices
sparse random linear network coding
Sparsity
Transfer matrices
ISSN:2169-3536, 2169-3536
Online Access:Get full text
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Summary:Sparse random linear network coding (SRLNC) is a promising solution for reducing the complexity of random linear network coding (RLNC). RLNC can be modeled as a linear operator channel (LOC). It is well known that the normalized channel capacity of LOC is characterized by the rank distribution of the transfer matrix. In this paper, we study the rank distribution of SRLNC. By exploiting the definition of linear dependence of the vectors, we first derive a novel approximation to the probability of a sparse random matrix being non-full rank. By using the Gauss coefficient, we then provide a closed approximation to the rank distribution of a sparse random matrix over a finite field. The simulation and numerical results show that our proposed approximation to the rank distribution of sparse matrices is very tight and outperforms the state-of-the-art results, except for the finite field size and the number of input packets are small, and the sparsity of the matrices is large.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2019.2907005