Coding for Modern Distributed Storage Systems IV

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Covers regenerating codes, then formalizes locality R (a symbol reconstructible from R others) and proves the distance tradeoff that generalizes the Singleton bound, showing nontrivial locality forces loss of global fault tolerance; describes practical constructions (Pyramid splitting, Tam–Barg gives polynomial field-size LRCs) and the open maximally-recoverable problem. Introduces availability T and shows resolvable combinatorial designs give n^{1/3} parallel reads with rate →1; gives a girth‑8 graph construction and simple greedy decoding for multiset batch reads. Open: MR codes, finite‑field Reed–Solomon repair and subpacketization benefits.

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" chapters (18)

1. 0:00Coding for Distributed Storage
2. 0:34Overview
3. 2:33Minimum Distance
4. 3:03Locality of a code
5. 3:46Example: code with message locality 5
6. 10:13Two easy pieces
7. 13:13Locality-distance tradeoff
8. 14:15All-symbol locality
9. 19:09Code Locality r, Code Availability t
10. 19:45Example of Locality r and availability t for symbol 1
11. 21:06message availability 2 (=2 parallel reads for a block)
12. 23:32Example: 3 replication
13. 28:06Resolvable Combinatorial designs
14. 30:35Code constructions
15. 34:35Multiset Batch codes (ongoing work)
16. 38:10Simple way to create Batch codes
17. 43:46Which repair metric to optimize?
18. 44:33Open problems