Lesson 200
Error-Correcting Codes
Parity · Hamming distance · Hamming(7,4)
1:00How adding structured redundancy lets data survive noise — from parity bits to Hamming codes to Reed-Solomon — without ever resending.
By the end, you can
- Explain why a single parity bit can detect but not correct errors, and identify the two-flip blind spot.
- Define Hamming distance and compute it for any two binary strings.
- Apply the formulas to find how many errors a code with minimum distance d can detect and correct.
- Identify the parity-bit positions in a Hamming(7,4) codeword and describe which data positions each covers.
- Encode a 4-bit data word into a Hamming(7,4) codeword by computing each parity bit via XOR.
- Decode a received Hamming(7,4) word by computing the syndrome and using it to locate and correct a single-bit error.
- Distinguish the application domains of parity, CRC, Hamming, Reed-Solomon, and capacity-approaching codes.
- Explain why Hamming(7,4) is more efficient than a 3-repetition code for single-bit correction.
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