Majority logic decoding

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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.


  1. Rice University,