Error-Detecting and Error-Correcting Codes
Error-control codes add redundant bits to protect messages against changes during transmission or storage.
Summary
Error-control codes add redundant bits to protect messages against changes during transmission or storage. A binary block code converts a message of bits into a codeword of bits, adding redundant bits. Its code rate is , the fraction of transmitted bits that represent message bits.
🧠 Key Concepts
- Binary block codes
- Redundant bits
- Hamming distance
- Minimum distance
- Error detection
- Error correction
- Parity checks
- Hamming codes
- Code rate
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Error-Detecting and Error-Correcting Codes
📘 Overview Error-control codes add redundant bits to a message so that changes during transmission or storage can be detected or corrected. For binary codes, the minimum Hamming distance between valid codewords determines the guaranteed protection against bit errors.
🧠 Key Idea Detection identifies a received pattern as invalid; correction identifies the original codeword. Greater separation between valid codewords allows more errors to be detected or corrected reliably.
⚔️ Core Details: - A binary block code maps each message of bits to a codeword of bits, adding
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