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This paper studies the effect of optimal power allocation on the performanceof communication systems utilizing automatic repeat request (ARQ). ConsideringType-I ARQ, the problem is cast as the minimization of the outage probabilitysubject to an average power constraint. The analysis is based on some recentresults on the achievable rates of finite-length codes and we investigate theeffect of codewords length on the performance of ARQ-based systems. We showthat the performance of ARQ protocols is (almost) insensitive to the length ofthe codewords, for codewords of length $\ge 50$ channel uses. Also, optimalpower allocation improves the power efficiency of the ARQ-based systemssubstantially. For instance, consider a Rayleigh fading channel, codewords ofrate 1 nats-per-channel-use and outage probability $10^{-3}.$ Then, with amaximum of 2 and 3 transmissions, the implementation of power-adaptive ARQreduces the average power, compared to the open-loop communication setup, by 17and 23 dB, respectively, a result which is (almost) independent of thecodewords length. Also, optimal power allocation increases the diversity gainof the ARQ protocols considerably.

Green communication via Type-I ARQ: Finite block-length analysis