Ultra reliable communication via CC-HARQ in finite block-length

In this paper, we suggest a power allocation strategy for the Chase Combining Hybrid Automatic Repeat Request (CC-HARQ) protocol with ultra-reliability constraints. The proposed optimal power allocation scheme would allow us to reach any outage probability target in the finite block-length regime. We cast an optimization problem as minimization of the average transmitted power under a given outage probability and maximum transmit power constraint. To solve the problem and attain the closed form solution, we utilize the Karush-Kuhn-Tucker (KKT) conditions. We show that in the finite block-length regime the transmitted power is highly dependent on the number of channel uses. However, as the block size increases, the transmitted power becomes constant. Furthermore, we show that by using the proposed power allocation scheme, we can achieve very large average and sum power gains when compared to the one shot transmission.