Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength

This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output fading channels, with and without channel state information at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular 1 × 2 single-input multiple-output Rician fading channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared with the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds.This work was supported in part by the Swedish Research Council under grant 2012-4571, by the Ericsson Research Foundation under grant FOSTIFT- 12:022, by a Marie Curie FP7 Integration Grant within the 7th European Union Framework Programme under Grant 333680, by the Spanish government (TEC2009-14504-C02-01, CSD2008-00010, and TEC2012-38800-C03-01), and by the National Science Foundation under Grant CCF-1253205. The material of this paper was presented in part at the 2013 and 2014 IEEE International Symposium on Information Theory