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.
For example, if we have a (3,1) repetition code, then encoding the signal m = 101001 yields a code c = 111000111000000111.
[edit] Repetition Decoder
Repetition decoding is done using Majority logic detection. To determine the value of a particular bit, we look at the received copies of the bit in the stream and choose the value that occurs more frequently.
For example, suppose we have a (3,1) repetition code and we are decoding the signal c = 110001111. The decoded message is m = 101, as we have most occurrence of 1's (two to one), 0's (two to one), and 1's (three to zero) in the first, second, and third code sequences, respectively.
[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] Repetition 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 ![\left[\frac{n}{2}\right]](../../../../math/a/f/a/afa54cdbf7266d5c0042ce82929f9b76.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.
