Noisy Channel, explained.
A noisy channel can corrupt a transmitted message. Error-correcting codes add structured redundancy so a receiver can recover information despite some errors.
Why it happens
Repeating a bit three times allows a majority vote to correct a single flipped bit. With independent errors below a one-half probability, this can reduce the final error rate. The improvement costs extra transmission capacity.
Redundancy can protect a message from independent transmission errors.
Read the result
Compare the raw message with the decoded repeated message at the same noise level. Check both recovered accuracy and the amount of redundancy, rather than judging accuracy alone.
A worked example
Sending one bit three times
You want to transmit 1, so the repetition code sends 111.
Noise changes it to 101. Majority voting still decodes it as 1.
Two flips would defeat this correction. Redundancy protects against a specified class of errors, not every possible failure.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A raw bit is wrong with chance p. Repeating it three times and taking the majority is wrong with chance 3p²−2p³, assuming independent flips. A seeded sample transmits one three-bit word.
Where this idea is useful
A practical use
Error-correcting codes help messages survive imperfect storage or communication.
A common misconception
“Repeating a message always guarantees delivery.”
Multiple errors, correlated failures, or sufficiently strong noise can still break a code. The simple repetition model is not an optimal communication system.
What this explanation leaves out
- Triple repetition is inefficient and assumes independent bit errors; real codes and channels are more complex.
Why not add unlimited repetition?
Each added copy uses bandwidth and time. Better codes can distribute redundancy more efficiently than repeating every bit.
What failures should a message survive, and how much extra capacity can you afford?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.