Method for performing soft decision decoding of Euclidean space Reed-Muller codes

摘要

Soft decision decoding of a codeword of a Reed-Muller (RM) code byselecting an optimal decomposition variable i using a likelihood calculation. A code RM(r, m) is expressed as {(u, uv)|uεRM(r, m−1) and vεRM(r−1, m−1)}, where uv denotes a component-wise multiplication of u and v, and (u, uv)=(r¹, r²). A receive codeword is separated into r¹=u and r²=uv based on the optimal decomposition variable, and r² is decoded according to the optimal decomposition variable, using a RM(r−1, m−1) decoder to obtain a decoded v and a first set of decoded bits. The decoded v is combined with r¹ using (r¹+r²v)/2, and(r¹+r²v)/2 is decoded using a RM(r, m−1) decoder to obtain a decoded u and a second set of decoded bits.