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.

Theory

, an odd number.

is the error over the transmission channel.

Algorithm

, an odd number.

• Hamming weight of the repetition code.

• , decode code word to be all 0's

• , decode code word to be all 1's

This algorithm is a boolean function in its own right, the majority function.

Example

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.

References

1. Rice University, https://web.archive.org/web/20051205194451/http://cnx.rice.edu/content/m0071/latest/