This work considers space-time channel coding for systems with multiple-transmit and a single-receive antenna, over space uncorrelated block-fading (quasi-static) channels. Analysis of the outage probability over such channels reveals the existence of a threshold phenomenon. The outage probability can be made arbitrary small by increasing the number of transmit antennas, only if the Eb/N0 is above a threshold which depends on the coding rate. Furthermore, it is shown that when the number of transmit antennas is increased, the ε-capacity of a block-fading Rayleigh channel tends to the Shannon capacity of an additive white Gaussian noise channel. This paper also presents space-time codes constructed as a serial concatenation of component convolutional codes separated by an interleaver. These schemes provide full transmit diversity and are suitable for iterative decoding. The rate of these schemes is less than 1 bit/s/Hz, but can be made arbitrary close to 1 bit/s/Hz by the use of Wyner-Ash codes as outer components. Comparison of these schemes with structures from literature shows that performance gains can be obtained at the expense of a small decrease in rate. Computer simulation results over block-fading Rayleigh channels show that the frame-error rate of several of these schemes is within 2-3 dB from the theoretical outage probability.