Which code is famous for its ability to correct single-bit errors in small blocks?

Which code is famous for its ability to correct single-bit errors in small blocks?

• A. Hamming code
• B. Reed-Solomon code
• C. Convolutional code
• D. Shannon limit

Answer: (A)

Single-bit errors in small data blocks are best handled by a parity-based block code that can pinpoint the exact faulty bit and fix it. Hamming codes do this by placing parity bits at positions that are powers of two and calculating a syndrome from the parity checks. That syndrome directly identifies the location of a single erroneous bit, so you can flip that bit to correct the error. The distance of these codes is three, which guarantees single-bit errors can be corrected, while many two-bit errors can be detected. A classic example is the 7-bit Hamming code that encodes 4 data bits with 3 parity bits, illustrating how small blocks can be protected against a single error. Reed-Solomon codes, in contrast, are excellent for correcting burst errors over larger blocks; convolutional codes are suited for continuous streams with decoding across sequences; and the Shannon limit is a theoretical bound rather than a concrete code.

Single-bit errors in small data blocks are best handled by a parity-based block code that can pinpoint the exact faulty bit and fix it. Hamming codes do this by placing parity bits at positions that are powers of two and calculating a syndrome from the parity checks. That syndrome directly identifies the location of a single erroneous bit, so you can flip that bit to correct the error. The distance of these codes is three, which guarantees single-bit errors can be corrected, while many two-bit errors can be detected. A classic example is the 7-bit Hamming code that encodes 4 data bits with 3 parity bits, illustrating how small blocks can be protected against a single error.

Reed-Solomon codes, in contrast, are excellent for correcting burst errors over larger blocks; convolutional codes are suited for continuous streams with decoding across sequences; and the Shannon limit is a theoretical bound rather than a concrete code.