Geo-Dispersed Erasure Coding Deep Dive

dewDrive incorporates an optional Geo-Dispersed Erasure Coding engine that distributes encrypted snapshot chunks across multiple independent cloud providers (AWS S3, Wasabi, Backblaze B2, and local on-premise nodes).

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#1. Mathematical Formulation: Reed-Solomon in $GF(2^8)$

Traditional 3x replication incurs a 200% storage overhead. dewDrive utilizes Reed-Solomon $RS(K, M)$ erasure coding built over the Galois Field $GF(2^8)$ using a generator matrix derived from a Cauchy distribution:

$$C_{i,j} = \frac{1}{x_i \oplus y_j}$$

Where:

• $K = 4$: Number of raw data shards.
• $M = 2$: Number of parity shards.
• Total Shards $N = K + M = 6$.
• Storage Overhead: $\frac{M}{K} = \frac{2}{4} = 50%$ (compared to 200% for 3x replication).

Payload Block [ 64 MB ]
      │
      ├─► Shard D1 (16 MB) ──► Node A: AWS us-east-1
      ├─► Shard D2 (16 MB) ──► Node B: Wasabi eu-central-1
      ├─► Shard D3 (16 MB) ──► Node C: Backblaze us-west-4
      ├─► Shard D4 (16 MB) ──► Node D: Local On-Premise NAS
      ├─► Shard P1 (16 MB) ──► Node E: GCP europe-west3
      └─► Shard P2 (16 MB) ──► Node F: Scaleway fr-par

Any 4 of 6 shards are mathematically sufficient to reconstruct the entire 64MB original payload through Gaussian elimination in $GF(2^8)$. Even if two complete cloud providers suffer simultaneous catastrophic outages, your data is fully recoverable in real time without downtime.

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#2. Interactive Visualizer

Experience the live interactive simulation in your browser: Visit the Geo-Dispersed Erasure Coding Visualizer to simulate node dropouts, Cauchy parity calculations, and real-time reconstruction.