RAID Architectures

Abstract

Redundant Array of Inexpensive Disks (RAID) combines multiple physical storage drives into a single logical storage unit managed by the operating system or dedicated hardware controllers. RAID architectures leverage data striping, mirroring, or bitwise parity to achieve higher I/O throughput, increased storage capacity, and fault tolerance against drive failure.

• Category: Distributed Storage & Reliability
• Core Objectives: High throughput, increased capacity, and fault recovery.
• Mathematical Foundation: Bitwise XOR ($\otimes$) parity calculations.

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RAID Level 0: Striping (Performance)

RAID 0 splits data sequentially into blocks and stripes them round-robin across $N$ physical drives:

• Read / Write Throughput: Multiplied by up to $N$ times through parallel drive access.
• Storage Efficiency: $100\%$ ($N$ disks provide $N\times \text{Capacity}$).
• Fault Tolerance: Zero ($0$). If a single drive fails, the entire array’s data is lost.

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RAID Level 1: Mirroring (Redundancy)

RAID 1 maintains identical copies of all data on secondary mirror drives:

• Read Throughput: Enhanced; reads can be serviced in parallel from either drive.
• Write Throughput: Slightly constrained; writes must update both physical disks simultaneously.
• Storage Efficiency: $50\%$ ($2N$ disks yield $N\times \text{Capacity}$).
• Fault Tolerance: High; survives the complete failure of any single drive in a mirrored pair.

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RAID Level 4: Dedicated Parity Disk (XOR Reconstruction)

RAID 4 stores data blocks striped across $N-1$ data drives while dedicating a single disk exclusively to store bitwise Parity ($P$):

Bitwise Parity Mathematics

Parity is calculated by evaluating the bitwise XOR ($\otimes$) across matching blocks on all data disks:

$P=A\otimes B\otimes C\otimes D$

By definition of XOR arithmetic, combining all data blocks and the parity block yields zero:

$(A\otimes B\otimes C\otimes D\otimes P)==0$

Fault Recovery Walkthrough

If Disk $C$ fails physically, its data is reconstructed by XORing the surviving data disks together with the parity disk:

$C=A\otimes B\otimes D\otimes P$

graph LR
    D0["Disk A (Alive)"] --> XOR["Bitwise XOR Engine"]
    D1["Disk B (Alive)"] --> XOR
    D3["Disk D (Alive)"] --> XOR
    DP["Disk P (Parity Alive)"] --> XOR
    XOR --> Rec["Reconstructed Disk C"]

Performance Bottleneck: The Parity Write Penalty

Because every write operation to any data disk requires updating the dedicated parity disk, the parity drive becomes a severe bottleneck under concurrent write workloads. Modern systems use RAID 5 (Distributed Parity) to rotate parity blocks evenly across all drives.

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RAID Level Trade-Off Summary

RAID Level	Structural Pattern	Minimal Disks	Capacity Utilization	Fault Tolerance	Primary Use Case
RAID 0	Striping	2	$100\%$ ($N$)	None (0 drive failures)	High-performance scratch storage
RAID 1	Mirroring	2	$50\%$ ($\frac{N}{2}$)	1 drive per mirrored pair	Mission-critical OS boot drives
RAID 4	Dedicated Parity	3	$\frac{N-1}{N}$	1 drive failure	Read-heavy redundant arrays

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Related Notes

• Hard Disk Drive Mechanics & Scheduling
• Solid State Drives & NAND Flash
• Dual-Mode Operation & Memory Protection