# Optimum Power Control at Finite Blocklength Journal article, 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.

Finite blocklength regime

outage probability

power control

truncated channel inversion

## Author

### Wei Yang

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

### Giuseppe Caire

University of Southern California

### Giuseppe Durisi

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

### Yury Polyanskiy

Massachusetts Institute of Technology (MIT)

#### IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 61 9 4598-4615

Information and Communication Technology

### Subject Categories

Telecommunications

### DOI

10.1109/TIT.2015.2456175