  Motivated by the current interest in ultra-reliable, low-latency,
machine-type communication systems, we investigate the tradeoff between
reliability, throughput, and latency in the transmission of information over
multiple-antenna Rayleigh block-fading channels. Specifically, we obtain
finite-blocklength, finite-SNR upper and lower bounds on the maximum coding
rate achievable over such channels for a given constraint on the packet error
probability. Numerical evidence suggests that our bounds delimit tightly the
maximum coding rate already for short blocklengths (packets of about 100
symbols). Furthermore, our bounds reveal the existence of a tradeoff between
the rate gain obtainable by spreading each codeword over all available
time-frequency-spatial degrees of freedom, and the rate loss caused by the need
of estimating the fading coefficients over these degrees of freedom. In
particular, our bounds allow us to determine the optimal number of transmit
antennas and the optimal number of time-frequency diversity branches that
maximize the rate. Finally, we show that infinite-blocklength performance
metrics such as the ergodic capacity and the outage capacity yield inaccurate
throughput estimates.
