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
$[n, k, d \ge 2k-2]$	Rashmi-Shah-Kumar
$[n, k, d \ge 2k-2]$	Lin-Chung
$[n=k+2$ and $k+3, k, d=n-1]$	Cadambe-Huang-Jafar-Li
$[n=k+2, k, d=n-1]$	Papailiopoulos-Dimakis-Cadambe
$[n=k+2, k, d=n-1]$	Tamo-Wang-Bruck
$[n, k, d=n-1 \ge 2k-1]$	Suh-Ramchandran
$[n, k, d=n-1 \ge 2k-1]$	Shah-Rashmi-Kumar-Ramchandran
$[n=5, k=3, d=4]$	Cullina-Dimakis-Ho
$[n=5, k=3, d=4]$	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 $(n=d+r, d \ge k, r \ge 1)$	Jiekak-Le Scouarnec
Minimum Bandwidth $(n\ge d+r, d \ge k, r \ge 1)$	Wang-Zhang
Minimum Storage $(n \ge d+r, k=d)$	Shum
Minimum Storage $(n=d+r, k=2, d \ge k, r=2)$	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
Repair-By-Transfer	Lin-Chung
DRESS Codes	Pawar-Noorshams-El Rouayheb-Ramchandran

Other Codes for Efficient Node Repair

Code	Authors
Hierarchial Codes	Duminuco-Biersack
Hierarchial Codes	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

Erasure Coding for Distributed Storage Wiki

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Explicit Codes

Exact-MSR Codes

Exact-MBR Codes

Cooperative Repair Codes

Uncoded Repair (Repair-by-Transfer) Codes

Other Codes for Efficient Node Repair

Erasure Coding for Distributed Storage Wiki

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Contents

How to use

External Links

−Table of Contents

Explicit Codes

Exact-MSR Codes

Exact-MBR Codes

Cooperative Repair Codes

Uncoded Repair (Repair-by-Transfer) Codes

Other Codes for Efficient Node Repair

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