1. © 2012 A. Datta & F. Oggier, NTU Singapore Redundantly Grouped Cross-object Coding for Repairable Storage Anwitaman Datta & Frédérique Oggier NTU Singapore APSYS 2012, Seoul http://sands.sce.ntu.edu.sg/CodingForNetworkedStorage

2. © 2012 A. Datta & F. Oggier, NTU Singapore Distributed Storage Systems What is this work about? Huge volume of data Scale-outC’est la vie Failures are inevitable! Fault-tolerance Overheads Erasure coding Over time Repairing lost redundancy Redundancy The story so far …

3. © 2012 A. Datta & F. Oggier, NTU Singapore What is this work about? The story so far … B2B2 B1B1 BnBn n encoded blocks … … Lost block Retrieve some k” blocks (k”=2…n-1) to recreate a lost block BxBx Re-insert Reinsert in (new) storage devices, so that there is (again) n encoded blocks Design space – Repair fan-in k’’ – Data tx. per node – Overall data tx. – Storage per node –…–… (n,k) code BxBx

4. © 2012 A. Datta & F. Oggier, NTU Singapore Related works A non-exhaustive list An Overview of Codes Tailor-made for Networked Distributed Data Storage Anwitaman Datta, Frederique Oggier arXiv:1109.2317 Codes on codes e.g. Hierarchical & Pyramid codes Locally repairable codes e.g. Self-repairing codes Network coding e.g. Regenerating codes Array codes … Most of these codes look at design of new codes with inherent repairability properties. This work: An engineering approach – can we achieve good repairability using existing (mature) techniques? (Our solution is similar to “codes on codes”)

5. © 2012 A. Datta & F. Oggier, NTU Singapore Separation of concerns Two distinct design objectives for distributed storage systems – Fault-tolerance – Repairability Related works: Codes with inherent repairability properties – Achieve both objectives together There is nothing fundamentally wrong with that – E.g., We continue to work on self-repairing codes This work: An extremely simple idea – Introduce two different kinds of redundancy Any (standard) erasure code – for fault-tolerance RAID-4 like parity (across encoded pieces of different objects) – for repairability

6. © 2012 A. Datta & F. Oggier, NTU Singapore Redundantly Grouped Cross-object Coding (RGC) e 11 e 21 e m1 p1p1 … e 12 e 22 e m2 p1p1 … e 1k e 2k e mk pkpk … … e 1k+1 e 2k+1 e mk+1 p k+1 … e 1n e 2n e mn pnpn … … Erasure coding of individual objects RAID-4 of erasure coded pieces of different objects

7. © 2012 A. Datta & F. Oggier, NTU Singapore RGC repairability Choosing a suitable m < k – Reduction in data transfer for repair – Repair fan-in disentangled from base code parameter “k” Large “k” may be desirable for faster (parallel) data access Codes typically have trade-offs between repair fan-in, code parameter “k” and code’s storage overhead (n/k) However: The gains from reduced fan-in is probabilistic – For i.i.d. failures with probability “f” Possible to reduce repair time – By pipelining data through the live nodes, and computing partial parity

8. © 2012 A. Datta & F. Oggier, NTU Singapore RGC repairability (and storage overhead ρ)

9. © 2012 A. Datta & F. Oggier, NTU Singapore Parameter “m” choice Smaller m: lower repair cost, larger storage overhead Is there an optimal choice of m? If so, how to determine it? – A rule of thumb: rationalized by r simultaneous (multiple) repairs – E.g. for (n=15, k=10) code: m < 5 m = 3 or 4 implies – Repair bandwidth saving of 40-50% even for f = 0.1 Typically, in stable environments, f will be much smaller, and the relative repair gains much more – Relatively low storage overhead of 2x or 1.875x

10. © 2012 A. Datta & F. Oggier, NTU Singapore Storage overhead & static resilience

11. © 2012 A. Datta & F. Oggier, NTU Singapore Further discussions Possibility to localize repair traffic – Within a storage rack, by placing a whole parity group in same rack – Without introducing any correlated failures of pieces of the same object Many unexplored issues – Soft errors (flipped bits) – Object update, deletion, … – Non i.i.d./correlated failures

12. © 2012 A. Datta & F. Oggier, NTU Singapore Concluding remarks RAID-4 parity of erasure encoded pieces of multiple objects – Lowers the cost of data transfer for a repair – Reduces repair fan-in – Possibility to localize repairs (and save precious interconnect BW) w/o introducing correlated failures w.r.to a single object – Pipelining the repair traffic helps realize very fast repairs Since the repairing node’s I/O, bandwidth or compute does not become a bottleneck Also the computations for repair are cheaper than decoding/encoding – Retains comparable storage overhead for comparable static resilience if only erasure coding was used (surprisingly so!) At least for quite some specific code parameter choices we tried Opens up many interesting questions that can be investigated experimentally as well as theoretically http://sands.sce.ntu.edu.sg/CodingForNetworkedStorage