Majority logic decoding
In error detection and correction, majority logic decoding is a method to decode repetition codes, based on the assumption that the largest number of occurrences of a symbol was the transmitted symbol.
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 , where is the error over the transmission channel.
The code word is , where , an odd number.
- Calculate the Hamming weight of the repetition code.
- if , decode code word to be all 0's
- if , decode code word to be all 1's
In a code, if R=[1 0 1 1 0], then it would be decoded as,
- , , so R'=[1 1 1 1 1]
- Hence the transmitted message bit was 1.