Repetition code
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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 it is 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 in detail.
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[edit] 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.
[edit] 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 occurrence 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 occurrence 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 way of assuming least errors, in the channel.
[edit] Repetition Codes on Fading Channel
For fading channels repetition codes perform well with increasing repetition factor. In this figure , the coding gains for various repetition factors are seen.
[edit] Repetion Codes on Gaussian Channel
For the AWGN channels perform worse for longer repetition factors. In this figure , the coding gains are progressively worse with the increasing parameter.
[edit] Code parameters
The dmin = n for an (n,1) code. Even then, repetition code performs worse, as its error correcting capacity is ![[\frac{n}{2}]](../../../math/f/c/c/fcc75e4a97113e2409e85ec26ae68dc3.png)
not utilized in repetition decoding algorithms.
[edit] 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 as well.
