Table of Contents
Explicit Codes
A tabulation of explicit codes for distributed storage systems that address the problem of efficient repair of failed nodes.
Exact-MSR Codes
| Parameters [n, k, d] | Authors |
|---|---|
| [n, k, d ≥ 2k-2] | Rashmi-Shah-Kumar |
| [n=k+2 and k+3, k, d=n-1] | Cadambe-Huang-Jafar-Li |
| [n=k+2, k, d=n-1] | Papailiopoulos-Dimakis-Cadambe |
| Tamo-Wang-Bruck | |
| [n, k, d=n-1 ≥ 2k-1] | Suh-Ramchandran |
| Shah-Rashmi-Kumar-Ramchandran | |
| [n=5, k=3, d=4] | Cullina-Dimakis-Ho |
| Suh-Ramchandran | |
| [n=4, k=2, d=3] | Wang-Mateescu-Dimakis-Bruck |
(Cadambe-Jafar-Maleki and Suh-Ramchandran have shown asymptotic existence of exact-MSR codes for all [n, k, d], while Shah-Rashmi-Kumar-Ramchandran have shown the non-existence of scalar linear exact-MSR codes when d < 2k-3.)
Exact-MBR Codes
| Parameters [n, k, d] | Authors |
|---|---|
| all | Rashmi-Shah-Kumar |
| [n, k ,d=n-1] | Rashmi-Shah-Kumar-Ramchandran |
(Shah-Rashmi-Kumar-Ramchandran have shown non-existence of exact-repair codes at essentially all interior points on the storage-bandwidth tradeoff of regenerating codes.)
Cooperative Repair Codes
| Code | Authors |
|---|---|
| Minimum Bandwidth (k=d=n-r) | Shum-Hu |
| Minimum Bandwidth (n=d+r, d≥k, r≥1) | Jiekak-Le Scouarnec |
| Minimum Bandwidth (n≥d+r, d≥k, r≥1) | Wang-Zhang |
| Minimum Storage (n ≥ d+r, k=d) | Shum |
| Minimum Storage (n=d+r, k=2, d≥k, r=2) | Le Scouarnec |
“r” is the number of failed nodes repaired simultaneously.
Uncoded Repair (Repair-by-Transfer) Codes
| Code | Authors |
|---|---|
| Fractional Repetition Codes | El Rouyheb-Ramchandran |
| Repair-By-Transfer | Rashmi-Shah-Kumar-Ramchandran |
| DRESS Codes | Pawar-Noorshams-El Rouayheb-Ramchandran |
Other Codes for Efficient Node Repair
| Code | Authors |
|---|---|
| Hierarchial Codes | Duminuco-Biersack |
| Huang-Biersack-Peng | |
| Twin Codes | Rashmi-Shah-Kumar |
| Self-repairing Homomorphic codes | Oggier-Datta |
| Approximately-exact MSR Codes | Rashmi-Shah-Kumar-Ramchandran |
| ExR | Janakiram-Kadhe-Chandra |
