In this paper, a serial concatenation scheme comprising of low-density parity-check (LDPC) and space-time trellis codes (STTC) with transmit antenna selection (TAS) is considered. We analyze the frame error rate (FER) performance of this scheme over quasi-static and fast Rayleigh fading channels by computer simulations. It is shown that applying TAS further improves the performance of the serial concatenation LDPC-STTC. In particular, TAS provides diversity gain over quasi-static fading and coding gain over fast fading channels. Diversity gain over fast fading is improved by the LDPC decoding iterations.