Repetition code

In coding theory, the repetition code is one of the most basic error-correcting codes. In order to transmit a message over a noisy channel that may corrupt the transmission in a few places, the idea of the repetition code is to just repeat the message several times. The hope is that the channel corrupts only a minority of these repetitions. This way the receiver will notice that a transmission error occurred since the received data stream is not the repetition of a single message, and moreover, the receiver can recover the original message by looking at the received message in the data stream that occurs most often.

Because of the bad error correcting performance and the low ratio between information symbols and actually transmitted symbols, other error correction codes are preferred in most cases. The chief attraction of the repetition code is the ease of implementation.

In the case of a binary repetition code, there exist two code words - all ones and all zeros - which have a length of ${\displaystyle n}$. Therefore, the minimum Hamming distance of the code equals its length ${\displaystyle n}$. This gives the repetition code an error correcting capacity of ${\displaystyle {\tfrac {n-1}{2}}}$ (i.e. it will correct up to ${\displaystyle {\tfrac {n-1}{2}}}$ errors in any code word).

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