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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8672897/ |
| _version_ | 1819179471398240256 |
|---|---|
| author | Wenlin Chen Fang Lu Yan Dong |
| author_facet | Wenlin Chen Fang Lu Yan Dong |
| author_sort | Wenlin Chen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-22T21:58:55Z |
| format | Article |
| id | doaj.art-7a1e9ac7de1542a299d206a48a56aa75 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-22T21:58:55Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-7a1e9ac7de1542a299d206a48a56aa752022-12-21T18:11:11ZengIEEEIEEE Access2169-35362019-01-017438064381910.1109/ACCESS.2019.29070058672897The Rank Distribution of Sparse Random Linear Network CodingWenlin Chen0https://orcid.org/0000-0001-5766-4551Fang Lu1https://orcid.org/0000-0002-9491-4895Yan Dong2The School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, ChinaThe School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, ChinaThe School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, ChinaSparse 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.https://ieeexplore.ieee.org/document/8672897/Rank distributionsparse matricessparse random linear network coding |
| spellingShingle | Wenlin Chen Fang Lu Yan Dong The Rank Distribution of Sparse Random Linear Network Coding IEEE Access Rank distribution sparse matrices sparse random linear network coding |
| title | The Rank Distribution of Sparse Random Linear Network Coding |
| title_full | The Rank Distribution of Sparse Random Linear Network Coding |
| title_fullStr | The Rank Distribution of Sparse Random Linear Network Coding |
| title_full_unstemmed | The Rank Distribution of Sparse Random Linear Network Coding |
| title_short | The Rank Distribution of Sparse Random Linear Network Coding |
| title_sort | rank distribution of sparse random linear network coding |
| topic | Rank distribution sparse matrices sparse random linear network coding |
| url | https://ieeexplore.ieee.org/document/8672897/ |
| work_keys_str_mv | AT wenlinchen therankdistributionofsparserandomlinearnetworkcoding AT fanglu therankdistributionofsparserandomlinearnetworkcoding AT yandong therankdistributionofsparserandomlinearnetworkcoding AT wenlinchen rankdistributionofsparserandomlinearnetworkcoding AT fanglu rankdistributionofsparserandomlinearnetworkcoding AT yandong rankdistributionofsparserandomlinearnetworkcoding |