A transmitting apparatus and receiving apparatus of a multi-carrier system using multiple antennas is proposed. A linear complex field (LCF) encoder performs linear precoding of input signals to be transmitted using a linear complex matrix based on the number of antennas and the number of subcarriers, and a subcarrier allocator allocates a subcarrier to each precoded signal. A transmitter transmits the signals through the multiple antennas. In a receiving apparatus, a subcarrier de-allocator extracts a linear-precoded signal by de-allocating a subcarrier of the received signal, and an LCF decoder outputs a bit reliability of the received signal based on the number m of antennas and the number n of subcarriers. Performance may be improved by using space diversity using multiple antennas and frequency diversity using OFDMA, and system complexity may be reduced by using a lattice reduction and a 2-branch Chase decoder.