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 ${\displaystyle 0,1}$, if a ${\displaystyle (n,1)}$ repetition code is used, then each input bit is mapped to the code word as a string of ${\displaystyle n}$-replicated input bits. Generally ${\displaystyle n=2t+1}$, an odd number.

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