3 research outputs found
Explicit MDS Codes for Optimal Repair Bandwidth
MDS codes are erasure-correcting codes that can correct the maximum number of
erasures for a given number of redundancy or parity symbols. If an MDS code has
parities and no more than erasures occur, then by transmitting all the
remaining data in the code, the original information can be recovered. However,
it was shown that in order to recover a single symbol erasure, only a fraction
of of the information needs to be transmitted. This fraction is called
the repair bandwidth (fraction). Explicit code constructions were given in
previous works. If we view each symbol in the code as a vector or a column over
some field, then the code forms a 2D array and such codes are especially widely
used in storage systems. In this paper, we address the following question:
given the length of the column , number of parities , can we construct
high-rate MDS array codes with optimal repair bandwidth of , whose code
length is as long as possible? In this paper, we give code constructions such
that the code length is .Comment: 17 page