Evaluation of the rank of balanced random sparse matrices over residual fields used for erasure codes
Abstract: We consider random sparse n × m matrices over Finite Fields F[2k], F[p] (p prime), F[pk] (p prime), used for linear erasure codes. The matrices are balanced or are derived from balanced matrices via the erasure of rows. The entries are non-zero uniformly distributed values. The target of the thesis is to analyze and simulate the rank of the matrices and the recoverability depending on the number of entries, the size of the matrix, and the field size p^k. First, we analyze the rank of these matrices over varying finite field size. The analysis shows that the full rank probability increases with increasing field size, and converges to 1 − 1/q, for large field sizes q. Then we try to solve the rank problem analytically, coming up with a rank probability formula for small matrices. Lastly, the analytical approach provides the foundation for an automated approach, i.e., an algorithm, to solve the problem. The algorithm is the main result of this work. It is based on conclusions from the analytical analysis and calculations
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Notes
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Universität Freiburg, Masterarbeit, 2021
- Keyword
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Auslöschungskanal
Matrizenrechnung
Galois-Feld
Zufallsgraph
- Event
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Veröffentlichung
- (where)
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Freiburg
- (who)
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Universität
- (when)
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2021
- Creator
- DOI
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10.6094/UNIFR/176176
- URN
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urn:nbn:de:bsz:25-freidok-1761762
- Rights
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Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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25.03.2025, 1:46 PM CET
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Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
Time of origin
- 2021
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