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Hamming Code, Cascading Parity and Level2 RAID

In case multiple data are compared, it is possible to either use multiple parity bits, which results in better speed or else a cascading scheme, that is, one calculates the XOR value of the first two data, subsequently, the third bit can be compared against the XOR value from bits 1 and 2, the fourth bit against the second parity value and so forth. This can be computationally very intensive and is not suitable for extremely fast ECC mechanisms such as ECC on system memory. In HDD technology, however, this is acceptable and a classical example is the “Hamming Code” used in Level2 RAID. Level2 RAID uses bit-level striping, that is, every bit from each Byte is written to and read from an individual drive. Since in HDD technology, each Byte consists of 10 bits, the minimum number of drives for a Level2 RAID setup is 11 drives, 10 drives for the data and one drive for the parity bit. In this case, it is possible to use a single parity bit since the location of any failing drive within the cascade is known and, therefore, the value of the missing bit can be reconstructed by a “relatively simple” parity calculation (since only one of the two possible values will result in the correct parity value).

The advantage of Level2 RAID is that through parity information, full redundancy can be added to an array with the overhead of a single drive for the storage of the parity bits. In practice, this translates into a mere 10% increase in the number of drives or by extension, in the total storage space compared to a 100% increase required e.g. by Level 1 mirroring. Because of the high number of drives required for a baseline configuration and the rigid scheme, Level2 RAID has become almost extinct.

By doing the parity calculations from one drive to the next and then to the following, the parity value can be held to a single digit, which requires the knowledge of the exact position of a failing drive within the system in order to be able to reconstruct the missing value. This cascading parity calculation (numbers in red on the left side, top to bottom) is very computationally intensive and is no longer used in mainstream configurations.

Level3 and Level4 RAID

A further development in RAID technology was the introduction of Level3 or byte-level striping with added parity storage onto a dedicated drive. RAID Level3 can be extended to a block level striping (which is then called Level4), however, since with every update of a single drive within the array, the parity drive will have to be written to as well, the actual workload of the parity drive will be much higher than that of any of the data drives. Consequently, the wear and tear and, by extension, the failure rate of the parity drive will be statistically higher than that of the data drives.

In Level3 RAID, all data are distributed on a byte by byte level over the data drives and the parity values (red) for all bytes are written to a dedicated drive.

In Level4 RAID, all data are distributed on a block level over the data drives, meaning that smaller files may be written to a single drive, whereas larger files are distributed over several drives (depending on the block size). The parity values for all bytes are written to a dedicated drive.

A number of theoretical and practice-oriented studies have been conducted in the past to evaluate the performance of the different RAID levels in different environments and a comprehensive overview of the results and expectations can be found on the PC-Guide

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