Coding for Modern Distributed Storage Systems III

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" summary

Shows a concrete 4,2 MDS construction that repairs a single lost symbol by transferring 1.5 symbols using sub-packetization and interference alignment, and proves a cut argument (the cut-set bound) giving beta ≥ 1/2. Functional repair maps to multicast on an information‑flow graph so the optimal tradeoff region is achievable; exact repair hits practical barriers: current MSR (Minimum Storage Regenerating) codes need exponential sub‑packetization and field size, Piggyback gives a practical but nonoptimal Hadoop implementation, and Reed‑Solomon repair gains so far are modest.

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" chapters (18)

1. 0:00Acknowledgments and disclaimers
2. 1:19Overview
3. 1:55Failures in a 3000 hadoop cluster (VLDB'13)
4. 5:54Storing information with linear equations
5. 9:45The repair problem.
6. 12:57Exact Repair-(4,2) example
7. 21:06Flow cutset bound
8. 21:33Information flow graph
9. 25:57The functional repair relaxation
10. 29:20Functional repair reduction to multicasting
11. 30:56Functional repair capacity
12. 32:03Storage-Bandwidth tradeoff
13. 32:29The infinite graph for Repair
14. 36:54Repair Bandwidth Tradeoff Region
15. 40:43Status in 2013
16. 43:12Open problem 1: What is the Exact repair region?
17. 50:46Open problem 2
18. 54:04Three repair metrics of interest