The seven-bit repair rack.
Can redundant bits repair a damaged message?
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Can redundant bits repair a damaged message?
Fit the code rack, parity comb and decoder.
Three even-parity checks place a seven-bit word inside a code whose valid words differ in at least three positions. The syndrome names a single flipped position. With two errors, that same single-error decoder can change the wrong bit and return the wrong data. The red limit is part of the lesson.
Even-parity Hamming (7,4), parity positions 1, 2 and 4; data positions 3, 5, 6 and 7, most significant first. Minimum distance three guarantees correction of one error. This decoder can miscorrect two errors; no extra SECDED parity bit is present. Injected errors are known to the simulator, not to the decoder.
Recover four data bits after exactly one transmitted bit flips.
Correct one flipped bit and test the two-error limit.