## MBR Codes

Optimal bandwidth efficiency codes are called minimum-bandwidth regenerating (MBR) and attain one of the two extremal points of the optimal Storage-Bandwidth Tradeoff curve [1] .

MBR codes require minimum repair-bandwidth - a replacement node downloads precisely that data which it wants to store, i.e., $d\beta = \alpha$. MBR codes then optimize the amount of storage under this condition as $B = k\alpha - \frac{k(k - 1)}{2}\beta$. (See here for the system model and notation.)

When a replacement node is constrained to store the same data as the corresponding failed node, the code is known as an exact-MBR code.

Results on MBR Codes (in chronological order)

Exact-repair MBR codes:

1. Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage (Rashmi, Shah, Kumar, Ramchandran) presents explicit codes for [n = d+1, k, d]. This code performs repair-by-transfer (also called uncoded-repair).

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