Non-standard RAID levels

Although all RAID implementations differ from the specification to some extent, some companies and open-source projects have developed non-standard RAID implementations that differ substantially from the standard. Additionally, there are non-RAID drive architectures, providing configurations of multiple hard drives not referred to by RAID acronyms.

Row diagonal parity (RDP) is a scheme where one dedicated disk of parity is in a horizontal "row" like in RAID 4, but the other dedicated parity is calculated from blocks permuted ("diagonal") like in RAID 5. The parity themselves can be laid out on fully dedicated disks (like double RAID 4) or in a distributed way (like in RAID 5).

RDP is invented by NetApp, which also uses it in an unusual system of parity storage called RAID-DP (RAID Double Parity). The "row" parity is stored on a dedicated disk like in RAID 4, but the "diagonal" parity is stored on a distributed way like in RAID 5. The technique can be considered RAID 6 in the broad SNIA definition and has the same failure characteristics as RAID 6.

RDP is very CPU-efficient compared to earlier schemes (Reed-Solomon with or without Anvin's optimization, EVENODD). The performance penalty of RAID-DP is typically under 2% when compared to a similar RAID 4 configuration.

RAID 7.m has been used to describe an erasure coding system with m extra drives and able to tolerate the loss of m drives. In this scheme, RAID 5 would be RAID 7.1 and RAID 6 would be RAID 7.2. Alternatively, RAID N+M refers to N regular data drives with M redundancy drives, being able to recover all the data when any M drives fail.

It is possible to support a far greater number of drives by choosing the parity function more carefully. The issue we face is to ensure that a system of equations over the finite field ${\displaystyle \mathbb {Z} _{2}}$ has a unique solution. To do this, we can use the theory of polynomial equations over finite fields.

Consider the Galois field ${\displaystyle GF(m)}$ with ${\displaystyle m=2^{k}}$. This field is isomorphic to a polynomial field ${\displaystyle F_{2}[x]/(p(x))}$ for a suitable irreducible polynomial ${\displaystyle p(x)}$ of degree ${\displaystyle k}$ over ${\displaystyle \mathbb {Z} _{2}}$. We will represent the data elements ${\displaystyle D}$ as polynomials ${\displaystyle \mathbf {D} =d_{k-1}x^{k-1}+d_{k-2}x^{k-2}+...+d_{1}x+d_{0}}$ in the Galois field. Let ${\displaystyle \mathbf {D} _{0},...,\mathbf {D} _{n-1}\in GF(m)}$ correspond to the stripes of data across hard drives encoded as field elements in this manner. We will use ${\displaystyle \oplus }$ to denote addition in the field, and concatenation to denote multiplication. The reuse of ${\displaystyle \oplus }$ is intentional: this is because addition in the finite field ${\displaystyle \mathbb {Z} _{2}}$ represents to the XOR operator, so computing the sum of two elements is equivalent to computing XOR on the polynomial coefficients.

A generator of a field is an element of the field such that ${\displaystyle g^{i}}$ is different for each non-negative ${\displaystyle i<m-1}$. This means each element of the field, except the value ${\displaystyle 0}$, can be written as a power of ${\displaystyle g.}$ A finite field is guaranteed to have at least one generator. Pick one such generator ${\displaystyle g}$, and define ${\displaystyle \mathbf {P} }$ and ${\displaystyle \mathbf {Q} }$ as follows: