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Optimal Rebuilding Access For Maximum Distance Separable Array Codes.pdf

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Preview of Optimal Rebuilding Access for Maximum Distance Separable Array Codes
🔗 Source: paradise.caltech.edu
📊 Size: 159 KB
📄 Pages: 6 pages
⬇️ Downloads: 84

Summary

The key question is how much information needs to be accessed to rebuild a single storage node after an erasure.

Problem Definition:

- Rebuilding Ratio: Defined as the fraction of remaining information accessed during rebuilding of a single erased node.
- MDS Array Codes: Use a 2D array where each column (node) stores either data or parity information. A code with `r` parity nodes is MDS if it can recover from any `r` erasures.

Previous Work and Open Problem:

- Previous research showed that an optimal rebuilding ratio of 1/r is achievable for rebuilding systematic nodes, but all parity nodes required full access. The open problem was constructing codes achieving the lower bound of 1/r for both systematic and parity nodes.

Main Contribution:

The paper presents new MDS array codes with `r` parity nodes that achieve the lower bound of 1/r for rebuilding any single systematic or parity node. These codes have efficient implementation, requiring simple computations within nodes, and straightforward encoding/decoding procedures.

Code Construction Details:

- The construction leverages permutations on the data elements to create zigzag sets in parity nodes, ensuring that each remaining element is part of at least one accessed zigzag set during rebuilding.
- Codes are constructed for specific `r` values (2 and 3) using finite fields of sizes 3 and 4, respectively.

Significance:

These codes offer optimal rebuilding ratios with simple implementations, improving the efficiency of data recovery in storage systems.

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Description

MDS array codes, commonly used in storage systems for error correction, aim to rebuild a single erased node with minimal access to redundant information, optimizing reconstruction efficiency for common single-erasure scenarios.

Technical Information

  • File Format: PDF
  • File Size: 159 KB
  • Pages: 6
  • Language: EN
  • Total Downloads: 84
  • Last Updated: 2 hours ago

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