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 finiteblocklength achievability and converse bounds. Index Terms-Channel dispersion, finite blocklength regime, MIMO channel, outage probability, quasi-static fading channel. 1 The term "quasi-static" is widely used in the communication literature (see, e.g., [2, Sec. 5.4.1], [3] ). The quasi-static channel model belongs to the general class of composite channels [1, p. 2631], [4] (also known as mixed channels [5, Sec. 3.3]). 0018-9448
Recently, the maximal achievable rate with given decoding error probability in the short blocklength regime was obtained in multiantenna quasi-static channel REF .
Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics