Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 60, Issue 7, Pages 4232-4265Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2318726
Keywords
Channel dispersion; finite blocklength regime; MIMO channel; outage probability; quasi-static fading channel
Funding
- Swedish Research Council [2012-4571]
- Ericsson Research Foundation [FOSTIFT-12:022]
- Marie Curie FP7 Integration Grant through the 7th European Union Framework Programme [333680]
- Spanish Government [TEC2009-14504-C02-01, CSD2008-00010, TEC2012-38800-C03-01]
- National Science Foundation [CCF-1253205]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1253205] Funding Source: National Science Foundation
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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 x 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.
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