Optimum Power Control at Finite Blocklength

• Published in: IEEE transactions on information theory Vol. 61; no. 9; pp. 4598 - 4615
• Main Authors: Yang, Wei, Caire, Giuseppe, Durisi, Giuseppe, Polyanskiy, Yury
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; AWGN channels; Channel coding; Communication channels; Electric noise; Error probability; Fading; Finite blocklength regime; Information theory; Normal distribution; outage probability; power control; Probability distribution; quasi-static fading channel; Random variables; Receivers; Receivers & amplifiers; Transmitters; truncated channel inversion; truncated channel inversion; power control; outage probability; Finite blocklength regime; quasi-static fading channel
• ISSN: 0018-9448; 1557-9654; 1557-9654
• DOI: 10.1109/TIT.2015.2456175

This paper investigates the maximal channel coding rate achievable at a given blocklength n and error probability ϵ, when the codewords are subjected 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 the cases, the second-order term is proportional to (n -1 ln n) 1/2 . For the quasi-static fading case, this second-order term is achieved by 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.