Modified Majority Logic Decoding of Reed-Muller Codes Using Factor Graphs

This study investigates the decoding algorithms of binary Reed–Muller (RM) codes. The main goal of the study is to modify majority-logic decoding using sum-product or min-sum decoding algorithms at the highest-order information bits in RM codes. Numerical results show that compared with the traditional majority-logic decoding algorithm, the modified majority-logic decoding method proposed in this study can reduce the bit error rate by a large margin. This is achieved without incurring a significant increase in decoding complexity because soft-decision decoding is only used in the highest information bits in RM codes whereas majority-logic decoding is still applied at the other orders of information bits in RM codes.