🛠️ What is Error Correction?

Unlike detection, error correction not only detects but also fixes the error without retransmission.

This is crucial in environments where:

  • Retransmission is costly or impossible (e.g., deep space, streaming media).
  • Timeliness is critical (e.g., real-time voice).

🧮 Hamming Code: The Foundation of FEC

Invented by Richard Hamming, this method introduces redundant parity bits into data to detect and correct single-bit errors.

👨‍🔬 How It Works:

  1. For k data bits, it adds r parity bits such that: [ 2^r \geq k + r + 1 ]

  2. Parity bits are placed at positions that are powers of 2.

  3. Each parity bit checks a subset of data bits.

  4. At the receiver:

    • Parity checks produce a syndrome.
    • If syndrome is 0 → no error.
    • If non-zero → indicates exact bit to flip.

🧠 Deep Insight

Hamming Code is error correction through structure. It treats data like a puzzle: a few extra pieces make the whole picture resilient to damage.

“The elegance of Hamming lies not in brute force, but in graceful anticipation of error.”

🧭 Applications

  • RAM (ECC memory)
  • Satellite communication
  • Embedded devices
  • Early data link protocols

🔗 Links