Quote:
Originally Posted by

**Elpee**
Can you guys explain in MORE DETAIL about "redundancy" and "parity "?

Thank you so much.

Let's play a game: I give you three slips of paper and two large numbers to remember. We'll call them A and B. The numbers are so big that even with your tiniest handwriting, you can only fit one number per slip of paper. After you have prepared, I will randomly remove one of your slips of paper and ask you to read both numbers back. If you had four slips, it would be easy-- just make two copies of both numbers, but with only three slips, you need to use a trick. Write down the following:

1) A

2) B

3) the sum of A and B

This way, no matter what slip I take, you are still left with enough information to compute both A and B. This general solution is extensible to more than 2 numbers:

1) A

2) B

3) C

4) D

5) A+B+C+D

Again, as long as I remove no more than one slip from your pile, you can always recalculate all the numbers. What if I tell you I'm going to take more than one slip away?

1) A

2) B

3) C

4) D

5) A+B+C+D

6) A+2B+3C+4D

No matter which two slips I take, you can always reconstruct everything with a little algebra. This pattern can extend as far as you want. If I were to take 3 slips, you'd need an additional slip with A+3B+5C+7D to keep up. These additional slips of paper act like parity drives. If there is a failure, parity drives let you keep your system running, albeit with degraded performance owing to the additional calculations needed. The actual implementation of parity calculation uses slightly different math, but the calculations are simple and, more importantly, relatively fast.

'Redundancy' means the number of extra drives you are using beyond the bare minimum needed to hold your data. Some people express it as a ratio between those two, other people just state the number of extra drives. Some people use the word 'tolerance', and some people will tell you that one word means the ratio and the other word means the count. Don't worry about the semantics; it's all the same concept.