PURPOSE: To easily make the number of an ideal point at a high speed by finding positions on plural planes according to a received signal and obtaining the number of the ideal signal point according to a mapping signal point.

CONSTITUTION: A controller 10 controls the whole modem and a ROM 111 is stored with a control program and various data. A CPU 111 obtains the positions of the received signal on plural planes by using the stored program and data. Further, a flag for a signal point Z is calculated and the signal point Z is mapped in an area of 0-π/4 to obtain the mapping signal point. A value D for partial decision making is obtained according to a transmission speed, and the signal point number N is determined on the basis of the flag (f) and decision value D. Then the addition of a circuit part is reduced and the ideal point N of the received signal can easily be obtained at a high speed.