3 research outputs found
A Unified Form of EVENODD and RDP Codes and Their Efficient Decoding
Array codes have been widely employed in storage systems, such as Redundant
Arrays of Inexpensive Disks (RAID). The row-diagonal parity (RDP) codes and
EVENODD codes are two popular double-parity array codes. As the capacity of
hard disks increases, better fault tolerance by using array codes with three or
more parity disks is needed. Although many extensions of RDP codes and EVENODD
codes have been proposed, the high decoding complexity is the main drawback of
them. In this paper, we present a new construction for all families of EVENODD
codes and RDP codes, and propose a unified form of them. Under this unified
form, RDP codes can be treated as shortened codes of EVENODD codes. Moreover,
an efficient decoding algorithm based on an LU factorization of Vandermonde
matrix is proposed when the number of continuous surviving parity columns is no
less than the number of erased information columns. The new decoding algorithm
is faster than the existing algorithms when more than three information columns
fail. The proposed efficient decoding algorithm is also applicable to other
Vandermonde array codes. Thus the proposed MDS array code is practically very
meaningful for storage systems that need higher reliability
Binary MDS Array Codes with Optimal Repair
Consider a binary maximum distance separable (MDS) array code composed of an
array of bits with information columns and parity
columns, such that any out of columns suffice to reconstruct the
information columns. Our goal is to provide {\em optimal repair access} for
binary MDS array codes, meaning that the bandwidth triggered to repair any
single failed information or parity column is minimized. In this paper, we
propose a generic transformation framework for binary MDS array codes, using
EVENODD codes as a motivating example, to support optimal repair access for
, where denotes the number of non-failed columns that
are connected for repair; note that when , some of the chosen
columns in repairing a failed column are specific. In addition, we show how our
transformation framework applies to an example of binary MDS array codes with
asymptotically optimal repair access of any single information column and
enables asymptotically or exactly optimal repair access for any column.
Furthermore, we present a new transformation for EVENODD codes with two parity
columns such that the existing efficient repair property of any information
column is preserved and the repair access of parity column is optimal
Multi-Layer Transformed MDS Codes with Optimal Repair Access and Low Sub-Packetization
An maximum distance separable (MDS) code has optimal repair access if
the minimum number of symbols accessed from surviving nodes is achieved,
where . Existing results show that the sub-packetization
of an high code rate (i.e., ) MDS code with optimal
repair access is at least . In this
paper, we propose a class of multi-layer transformed MDS codes such that the
sub-packetization is , where
, and the repair access is optimal for
any single node. We show that the sub-packetization of the proposed multi-layer
transformed MDS codes is strictly less than the existing known lower bound when
, achieving by restricting the choice
of specific helper nodes in repairing a failed node. We further propose
multi-layer transformed EVENODD codes that have optimal repair access for any
single node and lower sub-packetization than the existing binary MDS array
codes with optimal repair access for any single node. With our multi-layer
transformation, we can design new MDS codes that have the properties of low
computational complexity, optimal repair access for any single node, and
relatively small sub-packetization, all of which are critical for maintaining
the reliability of distributed storage systems