A full-diversity full-rate (FDFR) design was developed recently, to enable an uncoded layered space-time (LST) system to achieve full-diversity (NtNr) and full-rate (Nt symbols per channel use) simultaneously, for any number of transmit antennas Nt and receive antennas Nr. We investigate the performance of a coded FDFR system obtained by concatenating an error control coding (ECC) module and an FDFR module with a random interleaver in between. Iterative decoding is performed at the receiver. With Rc denoting the ECC rate, and d the minimum Hamming distance, an over-all transfer rate of RcNt symbols per channel use and a full diversity order dNtNr are achieved. Compared with coded V-BLAST, without sacrificing rate the coded FDFR system offers evident performance improvement when relatively weak codes are used. As Nr increases, even such a strong code as rate 1/2 turbo codes can benefit from FDFR. Specifically, 1.5 dB gain over coded V-BLAST is obtained in a 2 x 2 antenna setup when convolutional codes or rate 3/4 turbo codes are used. 0.5 dB gain is offered in a 2 x 5 setup when rate 1/2 turbo code is used. The price paid is increased complexity.