Optimum Power Control at Finite Blocklength
Artikel i vetenskaplig tidskrift, 2015

This paper investigates the maximal channel coding rate achievable at a given blocklength $n$ and error probability $\epsilon$, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-$n$ expansion of the maximal channel coding rate is characterized both for additive white Gaussian noise (AWGN) channels and for quasi-static fading channels with perfect channel state information available at both the transmitter and the receiver. It is shown that in both cases the second-order term is proportional to $\sqrt{n^{-1}\ln n}$. For the quasi-static fading case, this second-order term is achieved by \emph{truncated channel inversion}, namely, by concatenating a dispersion-optimal code for an AWGN channel subject to a short-term power constraint, with a power controller that inverts the channel whenever the fading gain is above a certain threshold. Easy-to-evaluate approximations of the maximal channel coding rate are developed for both the AWGN and the quasi-static fading case.

quasi-static fading channel

Finite blocklength regime

outage probability

power control

truncated channel inversion


Wei Yang

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk

Giuseppe Caire

University of Southern California

Giuseppe Durisi

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk

Yury Polyanskiy

Massachusetts Institute of Technology (MIT)

IEEE Transactions on Information Theory

0018-9448 (ISSN) 1557-9654 (eISSN)

Vol. 61 9 4598-4615 7156144


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