METHOD FOR PERFORMING SOFT DECISION DECODING OF EUCLIDEAN SPACE REED-MULLER CODE

PROBLEM TO BE SOLVED: To provide soft decision decoding of a codeword of a Reed-Muller (RM) code by selecting an optimal decomposition variable i using a likelihood calculation.SOLUTION: A code RM(r, m) is expressed as {(u, uv)|(u belongs to RM(r, m-1)) and (v belongs to RM(r-1, m-1))} where uv denotes a component-wise multiplication of u and v, and (u, uv)=(r, r). A received codeword is separated into r=u and r=uv based on the optimal decomposition variable, and ris decoded according to the optimal decomposition variable, using an RM(r-1, m-1) decoder to obtain a decoded v and a first set of decoded bits. The decoded v is combined with rusing (r+rv)/2, and (r+rv)/2 is decoded using an RM(r, m-1) decoder to obtain a decoded u and a second set of decoded bits.