Design of Majority-Logic Decoders for the Shortened Reed-Muller Code in TETRA

The attractiveness of majority-logic decoding is its simple implementation. However, it provides a modest amount of coding gain. A modified Massey´s majority-logic decoding algorithm is proposed to improve error-correcting performance. With hard-decision and soft-decision, the modified algorithm is applied to decode the (30,14) shortened Reed-Muller (RM) code in TETRA as well as syndrome algorithm, Massey´s majority-logic algorithm, and Rudolph´s majority-logic algorithm. Simulation results show that, the proposed modified algorithm can provide more coding gain than the original Massey´s algorithm, the modified scheme has the best performance of error correction among four hard-decision schemes, and the Rudolph´s scheme outperforms the other three schemes in the case of soft-decision.