Repetition code

Repetition code, is a $(n,1)$ coding scheme, that repeats the bits, across a channel to achieve error free communication. Repetition code, is generally a very naive method of encoding data across a channel, and its not preferred for Additive White Gaussian Channels(AWGN), due to its worse-than-the-present error performance.

There are, two parts to the repetition code, as for any other code: the encoder, and decoder, which will be described about in detail.

Repetition Coder

The encoder, is a simple device that repeats, $n$ times, a particular bit to the waveform modulator, when the bit is received from the source stream.

Eg: If we have a $(3,1)$ repetition code, then encoding the following signal, $m=101001$, yields, a code$c=111000111000000111$.

Repetition Decoder

Repetition decoding is done, using Majority logic detection. In this scheme, we select the transmitted bit, as the one that has the maximum occurance in the stream.

Eg: If we have a $(3,1)$ repetition code, then decoding the following signal, $c=110001111$, yields, a message$m=101$, as we have most occurance of 1's 0's and 1's in the first, second and third code sequences, received from the channel. This method is again a naive may of assuming least errors, in the channel.

Code parameters

The $d_{min}=n$ for an $(n,1)$ code. Even then, repetition code performs worse, as its error correcting capacity is $[{\frac {n}{2}}]$ not utilized in repetition decoding algorithms.

Applications

Due to the simplicity of the channel encoding, and decoding signals, for repetition codes,

they find applications, in fading channels, and non-AWGN environments. Repetition codes,

can be viewed as a method of space-time diversity aswell.

See Also

1. Majority Logic Decoding
2. Hamming code
3. Convolutional code