Delay-Optimal Coded Offloading for Distributed Edge Computing in Fading Environments

The rapid growth in scale and complexity of mobile applications fosters the development of the coded edge computing paradigm. By exploiting the redundancy in the encoded subtasks, coded edge computing enables collaborative transmission of multiple edge nodes and is promising for distributed computing in wireless fading environments. Nonetheless, to the best of our knowledge, due to challenges arising from the selection of the coding parameters, offloading strategy design for coded edge computing in general fading environments still remains open. With this consideration, the coded offloading problem is studied in this work and a delay-optimal coded offloading scheme is proposed. In particular, when the offloaded tasks are encoded by <inline-formula> <tex-math notation="LaTeX">$(k,r)$ </tex-math></inline-formula> linear codes, transmission diversity gains can be obtained by performing edge node selection to mitigate fading. However, the corresponding optimization problem turns out to be a highly non-trivial non-linear mixed-integer programming. To this end, through in-depth analysis based on order statistics, it is found that the average processing delay of the offloaded tasks admits a favorable <inline-formula> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula>-structure with respect to the coding parameter <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>, under arbitrary fading distribution. This key theoretic result allows us to efficiently solve the original problem using monotonic optimization. Simulations are conducted to validate our analysis and corroborate the effectiveness of the proposed scheme.