hesela.devMaximally recoverable code
A maximally recoverable code corrects every erasure pattern that is recoverable by some coefficient assignment within its prescribed parity topology.
The guarantee is relative to the topology. Local equations cannot protect symbols outside their support. A code may be maximally recoverable without offering the any-k survivor guarantee of an MDS code. Choosing a suitable finite field and coefficients is a separate requirement from describing the groups.
For data-local codes with one local parity per group and h global parities, Gopalan and colleagues characterize recovery by removing one coordinate per local group and requiring the remaining code to be MDS. Their Lemma 4 rules out an erasure set E touching t local groups when |E| exceeds t+h. This is an erasure statement with known missing locations, not an unknown-error correction guarantee. [1]
Relations
- related
- Locally repairable code, Erasure coding, Reed–Solomon codes (storage), Repair locality, Maximum distance separable code
Citations
- Gopalan et al. Explicit Maximally Recoverable Codes with Locality. IEEE TIT (2014), section II: Definition 3 and Lemma 4.
- Local repair is not whole-node repair: which four losses can be recovered?
Sources & caveats
- The companion enumerates two fixed topologies under the MR assumption; it does not implement or certify their coefficient construction. [2]