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The Rank Distribution of Sparse Random Linear Network Coding
- Source :
- IEEE Access, Vol 7, Pp 43806-43819 (2019)
- Publication Year :
- 2019
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2019.
-
Abstract
- 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.
- Subjects :
- General Computer Science
Rank (linear algebra)
sparse matrices
MathematicsofComputing_NUMERICALANALYSIS
General Engineering
020206 networking & telecommunications
02 engineering and technology
sparse random linear network coding
Transfer matrix
Rank distribution
Linear map
Channel capacity
Finite field
Linear network coding
0202 electrical engineering, electronic engineering, information engineering
General Materials Science
lcsh:Electrical engineering. Electronics. Nuclear engineering
lcsh:TK1-9971
Random matrix
Algorithm
Sparse matrix
Mathematics
Subjects
Details
- ISSN :
- 21693536
- Volume :
- 7
- Database :
- OpenAIRE
- Journal :
- IEEE Access
- Accession number :
- edsair.doi.dedup.....48cdd5a5dc999c47345669c70d3391b1