星期二, 10月 28, 2025

Hamming code

1. Sender: Encoding 2. Transmission & Error 3. Receiver: Correction Original Data (1011) 1 D3 0 D5 1 D6 1 D7 Encoded Codeword 0 P1 1 P2 1 D3 0 P4 0 D5 1 D6 1 D7 P1 checks D3, D5, D7 (1+0+1=even) P2 checks D3, D6, D7 (1+1+1=odd -> P2=1) P4 checks D5, D6, D7 (0+1+1=even) Transmitted: 0110011 Bit 6 flips! Received Codeword 0 1 1 0 0 0 1 Parity Re-check P1 (1,3,5,7): 0+1+0+1 = even ✔ P2 (2,3,6,7): 1+1+0+1 = odd ❌ P4 (4,5,6,7): 0+0+0+1 = odd ❌ Error Syndrome Failed checks are P2 and P4. Position 2 + Position 4 = Bit 6 Correction Flip bit at position 6. 0 1 1 0 0 1 1 Recovered Data 1 0 1 1
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