Dynamic Power Control for Delay-Optimal Coded Edge Computing

Coded edge computing is envisioned as a promising solution to cope with the ever-increasing large-scale and computation-intensive mobile applications. Besides alleviating the computation straggling issue, task encoding in coded edge computing is also beneficial to the transmission of computation results. Nonetheless, existing pioneering works in this direction mainly take an information-theoretical perspective and assume the ideal scenarios of high signal-to-noise ratio. To the best of our knowledge, the issue of power control still remains largely unexplored for coded edge computing. In this work, two novel power control schemes are developed for coded edge computing in dynamic wireless environments, which apply to the repetition encoded task computing and the general linearly encoded task computing, respectively. However, the corresponding optimization problems turn out to be non-convex and highly non-trivial. To this end, by exploiting the underlying structural property, a novel partition-based iterative optimization method is developed to obtain the closed-form expression of the optimal dynamic power control strategy for repetition encoded task computing. For the case of more general linearly encoded task computing, the corresponding problem is transformed into a sum-of-ratio problem and then solved iteratively. Simulations are conducted to corroborate the effectiveness of the proposed schemes.