Majority-logic decoding for the Reed-Muller code in TETRA

For the shortened RM code in TETRA, it is quite different from the classic RM codes. and Reed's majority-logic decoding algorithm is no longer applicable to it. According to the characteristics of orthogonal parity-check matrixes, an exhaustive algorithm was proposed to search for the orthogonal parity-check matrixes of general block codes. The exhaustive search algorithm was applied to the shortened RM code, and the searching speed was analyzed. This code was proved to be two-step completely orthogonalizable, and Massey's majority-logic decoding scheme for it was given. Simulation results show that the decoding scheme is superior to the syndrome decoding scheme with respect to the error-correcting performance, whether hard-decision or soft-decision is employed.