Description
An \((n,k,m)\) array code whose codewords can be recovered by any \(k\) out of \(n\) nodes, where each node stores a length-\(m\) column of the codeword. MDS array codes are MDS codes when each matrix codeword is treated as a vector by converting each column into a single coordinate via subpacketization.
Parent
Children
- B-code — B-codes are examples of MDS array codes [1].
- EVENODD code — EVENODD codes are examples of MDS array codes [1].
- Row-Diagonal Parity (RDP) code
- Star code
- X-code — X-codes are examples of MDS array codes [1].
- Ye-Barg code
- Zigzag code
- Minimum-storage regenerating (MSR) code — MSR codes are MDS array codes; e.g., see [2].
Cousins
- Maximum distance separable (MDS) code — MDS array codes are MDS codes when each matrix codeword is treated as a vector by converting each column into a single coordinate via subpacketization.
- Generalized EVENODD code — Generalized EVENODD codes for prime \(m\) and \(r=3\) are MDS array codes [3].
References
- [1]
- I. Tamo, Z. Wang, and J. Bruck, “Zigzag Codes: MDS Array Codes With Optimal Rebuilding”, IEEE Transactions on Information Theory 59, 1597 (2013) arXiv:1112.0371 DOI
- [2]
- V. Ramkumar, N. Raviv, and I. Tamo, “\(\varepsilon\)-MSR Codes for Any Set of Helper Nodes”, (2024) arXiv:2408.16584
- [3]
- M. Blaum, P. G. Farrell, H. C. A. van Tilborg, 1998. Array codes. Handbook of coding theory, 2 (Part 2), pp. 1855-1909.
Page edit log
- Victor V. Albert (2024-08-09) — most recent
Cite as:
“MDS array code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/mds_array