RAID — levels 0, 1, 5, 6, 10 — trade-offs: Foundations

4.2.39 · D1 · Coding › Operating Systems › RAID — levels 0, 1, 5, 6, 10 — trade-offs

Parent note padhne se pehle, tumhe kuch basic ideas ka ek chota sa toolbox chahiye: yahan disk ka matlab kya hai, block kya hota hai, striping/mirroring/parity pictures mein kya dikhte hain, aur algebra ka ek piece — XOR — jo parity ko magical banata hai. Hum inhe zero se build karte hain, ek aisi order mein jahan har naya idea sirf pehle wale ideas pe depend karta hai.

1. Disk — wo cheez jise hum protect kar rahe hain

Poora topic isliye exist karta hai kyunki ek box kaafi nahi hai. Ye word pehle chahiye kyunki "array of disks" (RAID mein A aur D) literally inhi kai boxes ko line up karna hai.

Recall Ek single disk slow aur fragile dono kyun hota hai?

Ek time pe ek hi head read/write karta hai (slow), aur agar wo fail ho jaaye toh koi doosri copy nahi hoti (fragile).

2. Block — wo unit jo hum move karte hain

Blocks ki zaroorat isliye hai kyunki RAID kabhi "poori file" ko "poore disk" pe nahi move karta — ye pages ko alag-alag disks pe move karta hai. Iske baad ka sab kuch (striping, parity) ek rule hai kaunsa page kahaan jaayega ke liye.

Figure — RAID — levels 0, 1, 5, 6, 10 — trade-offs

Figure dekho: ek file (tall stack) equal blocks $D_{1}, D_{2}, D_{3}, D_{4}$ mein slice hui hai. Wo blocks hi wo atoms hain jo hum disks ke across shuffle karte hain.

3. $n$ — kitne disks hain hamare paas

4. Striping — speed ke liye pages spread karna

Picture ye hai: ek door ki jagah, $n$ doors ek saath khule hain. Striping ki poori jeet yahi hai — parallelism — aur poora risk bhi — koi bhi ek disk kho jaaye toh wo pages hamesha ke liye khatam.

Left panel striping dikhata hai: har disk ek alag page hold karta hai (fast, no safety). Ye picture yaad rakhna — RAID 0 yahi picture hai.

5. Mirroring — survival ke liye copy

Usi figure ke right panel mein dekho: do disks same pages $D_{1}, D_{2}$ hold karti hain. Yahi redundancy hai isliye RAID 1 failure ke baad survive karta hai — aur isliye ye tumhara 50% space cost karta hai.

Recall Ek-ek line mein striping vs mirroring

Striping = har disk pe alag page (speed, no safety). Mirroring = ek hi page do baar (safety, half capacity).

6. XOR ( $\oplus$ ) — parity ke peeche ka algebra

Parity ek clever, sasta safety net hai, aur ye sirf ek operation pe chalta hai: XOR, jise $\oplus$ likha jaata hai. Hume ye symbol poori tarah se samajhna hoga, kyunki parent ka poora derivation isi pe depend karta hai. Deeper treatment ke liye XOR and Boolean Algebra dekho.

XOR kyun, plain addition kyun nahi? Kyunki XOR ke teen magic properties hain jo hume ise perfectly undo karne dete hain:

Figure dikhata hai kyun parity ek lost block recover karta hai: saare blocks ko ek "summary" $P$ mein XOR karo; jab ek block disappear ho jaata hai, toh survivors ko $P$ ke saath XOR karo aur har survivor $P$ ke andar apni copy cancel kar leta hai (the $x \oplus x = 0$ law), sirf missing block reh jaata hai. Yahi cancellation RAID 5 ke peeche ka poora trick hai.

7. $⨁$ aur subscripts — bada formula padhna

Toh parent ka recovery rule $D_{k} = P \oplus ⨁_{i \neq = k} D_{i}$ plain words mein padhta hai: "lost block = summary XOR har surviving block." Yahan kuch naya nahi hai — ye section 6 compactly likha gaya hai.

8. $P$ , $Q$ , aur $GF (2^{8})$ — ek parity vs do

$Q$ sirf ek aur XOR kyun nahi ho sakta? Kyunki do XOR summaries same equation do baar hogi — koi naya information nahi. $Q$ ko genuinely independent banane ke liye, RAID 6 Galois field $GF (2^{8})$ mein arithmetic use karke har block ko alag-alag weight karta hai (dekho Galois Fields GF(2^n)). Tumhe field ke internals yahan nahi chahiye — sirf ye idea: do alag recipes = do solvable equations = do disks recoverable.

Recall Ek doosra XOR RAID 6 ko uski double protection kyun nahi dega?

Do XOR summaries same equation encode karti hain; tum ek equation se do unknowns solve nahi kar sakte. $Q$ independent hone ke liye $GF (2^{8})$ use karta hai.

9. I/O — write ki cost count karna

Ye foundations topic ko kaise feed karte hain

Upar se neeche padho: atoms (disk, block, XOR) teen tools (striping, mirroring, parity) build karte hain, jo combine hokar paanch RAID levels banate hain.

Reliability and MTBF — kyun zyada disks matlab zyada failures plan karne ke liye.
Backups vs Redundancy — kyun RAID availability hai, backup nahi.
File Systems — wo layer jo logical disk ke upar baith jaati hai jo RAID present karta hai.
Parent pe wapas jaao: 4.2.39 RAID — levels 0, 1, 5, 6, 10 — trade-offs (index 4.2.39).

Equipment checklist

Khud test karo — tum parent note ke liye ready ho jab ye saab instantly aaye.

Is topic mein "disk" kya hai, aur uski do weaknesses?

Ek storage device with ek head — slow (ek door) aur fragile (koi copy nahi).

"Block" kya hota hai?

Data ka ek fixed-size chunk, jaise ek kitaab se ek page fada hua.

Symbol

n

ka matlab kya hai?

Array mein disks ki number.

Striping ek line mein bolo.

Parallel speed ke liye alag-alag disks ko alag blocks deal karo, koi redundancy nahi.

Mirroring ek line mein bolo.

Har disk ka identical twin copy rakho; tumhari aadhi capacity cost hoti hai.

1011 \oplus 0110

compute karo.

1101

Teen XOR laws batao.

x \oplus x = 0

x \oplus 0 = x

, order doesn't matter (commutative + associative).

Ek parity block exactly ek lost disk recover kyun karta hai?

XOR self-inverse hai, isliye survivors

P

ke andar cancel ho jaate hain, sirf missing block bachta hai — ek equation, ek unknown.

⨁_{i \neq = k} D_{i}

ka words mein matlab kya hai?

Disk

k

ke alawa har data block ko XOR karo.

RAID 6 ko

Q

ke liye

GF (2^{8})

ki zaroorat kyun hai doosre XOR ki jagah?

Doosra XOR same equation hai;

Q

ko do unknowns solve karne ke liye independent hona chahiye.

Ek "I/O" kya hai, aur hum inhe count kyun karte hain?

Ek disk se ek read ya write; ye slow part hote hain, isliye inhe count karna write penalty measure karta hai.