When precoding information corresponding to data items of respective layers to be transmitted is received from an upper layer, an encoding apparatus of a multiple input multiple output (MIMO) communication system selects a precoding matrix among a plurality of precoding matrices stored in a storage using the precoding information and precodes the data items of the respective layers by simple operations consisting of at least one operation combination of addition, subtraction, selection, and inversion operations in accordance with a kind of the selected precoding matrix and a precoding operation pattern.