Majority Logic Decoding - Theory

Theory

In a binary alphabet made of, if a repetition code is used, then each input bit is mapped to the code word as a string of -replicated input bits. Generally, an odd number.

The repetition codes can detect up to transmission errors. Decoding errors occur when the more than these transmission errors occur. Thus, assuming bit-transmission errors are independent, the probability of error for a repetition code is given by P_e = \sum_{k=\frac{n+1}{2}}^{n} {n \choose k} \epsilon^{k} (1-\epsilon)^{(n-k)}, where is the error over the transmission channel.

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