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# Optimum Power Control at Finite Blocklength

Wei Yang (Institutionen för signaler och system, Kommunikationssystem) ; Giuseppe Caire ; Giuseppe Durisi (Institutionen för signaler och system, Kommunikationssystem) ; Yury Polyanskiy
IEEE Transactions on Information Theory (0018-9448). Vol. 61 (2015), 9, p. 4598-4615.

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.

Nyckelord: Finite blocklength regime; outage probability; power control; quasi-static fading channel; truncated channel inversion

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CPL Pubid: 219909

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Institutionen för signaler och system, Kommunikationssystem (1900-2017)