Decoding for peak-power reduction and error-correction capabilities in multicarrier transmission

A multicarrier decoder comprising:

• an encoding unit both for determining, based on each input signal, a plurality of phases containing one or more kernels each consisting of first to fourth phases that satisfy a phase condition that an absolute value of difference of a phase difference Δθ(2k), between 2k−1 second phases and 2k−1 first phases, from a phase difference Δθ*(2k), between 2k−1 fourth phases and 2k−1 third phases, |Δθ(2k)−Δθ*(2k)|, be equal to a given value, where k is an integer not smaller than 1, and for generating a plurality of codes corresponding to said input signal by assigning said plurality of phases to a plurality of carrier frequencies in such a manner as to satisfy a carrier allocation that a difference of 2k−1 carrier frequencies to which said second phases are assigned from 2k−1 carrier frequencies to which said first phases are assigned be equal to a difference of 2k−1 carrier frequencies to which said fourth phases are assigned from 2k−1 carrier frequencies to which said third phases are assigned, carrier frequencies to which said third phases are assigned having the same carrier allocation as those of said first phases;
• a code distance calculating unit for calculating a code distance between each of said plurality of codes and a received code;
• and
• a smallest-distance code selecting unit for decoding said received code by determining an input signal that provides a code whose code distance to said received code is the smallest.