Repairing Reed-Solomon Codes via Subspace Polynomials
| Autor: | Son Hoang Dau, Thi Xinh Dinh, Olgica Milenkovic, Tran Thi Luong, Han Mao Kiah |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Physics Information Theory (cs.IT) Computer Science - Information Theory Dimension (graph theory) 020206 networking & telecommunications 02 engineering and technology Library and Information Sciences Computer Science Applications Combinatorics Redundancy (information theory) Reed–Solomon error correction 0202 electrical engineering electronic engineering information engineering Subspace topology Computer Science::Information Theory Information Systems |
| Zdroj: | IEEE Transactions on Information Theory. 67:6395-6407 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2021.3071878 |
| Popis: | We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature that employ trace polynomials. The Reed-Solomon codes are over $\mathbb {F}_{{q}^{\ell }}$ and have redundancy ${{r}} = {{n}}-{{k}} \geq {{q}}^{{m}}$ , $1\leq {{m}}\leq \ell $ , where ${{n}}$ and ${{k}}$ are the code length and dimension, respectively. In particular, for one erasure, we show that our schemes can achieve optimal repair bandwidths whenever ${{n}}={{q}}^\ell $ and ${{r}} = {{q}}^{{m}}$ , for all $1 \leq {{m}} \leq \ell $ . For two erasures, our schemes use the same bandwidth per erasure as the single erasure schemes, for $\ell /{{m}}$ is a power of ${{q}}$ , and for $\ell ={{q}}^{{a}}$ , ${{m}}={{q}}^{{b}}-1>1$ ( ${{a}} \geq {{b}} \geq 1$ ), and for ${{m}}\geq \ell /2$ when $\ell $ is even and ${{q}}$ is a power of two. |
| Databáze: | OpenAIRE |
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