QPSK Space-Time Turbo Codes

Recently, there has been a surge of interests, e.g., [2,3], in the design of so called “space-time” codes which take adv;antage of both the spatial diversity provided by multiple antennas and the temporal diversity available with time-varying fading. Design criteria [3-51 have been proposed for space-time codes in a variety of environments. In quasi-static Rayleigh fading channel, each possible code word difference in a linear coded modulation produces a “signal” matrix. Increasing the rank of a “signal” matrix increases the amount of diversity in demodulation and reduces the pairwise error probability [3,5]. If the code length in time, N,, is larger than the number of transmit antennas, Lt, the maximum possible rank of a “signal” matrix is Lt . A code is said to achieve full space diversity when the rank of every “signal” matrix correspondingto every code word pair is equal to Lt. While the ranks of the “signal” matrices are defined over the comp1.e~ number field, traditional code design is usually carried out in finite fields or finite rings. This discrepancy causes a serious obstacle in the design. The paper by Hammons and El Ganial [6] represents an important first step to bridge this discrepancy. They provided a binary rank criteria for binary BPSK codes and Z4 QPSK codes to ensure full space diversity. More recently, the design of PSK modulated space-time codes is also addressed by Blum [7]. In [8], we provide a theory for the design of space-time codes in quasi-static Rayleigh fading channel with higher order of con-