Adaptive Private Distributed Matrix Multiplication

We consider the problem of designing codes with flexible rate (referred to as rateless codes), for private distributed matrix-matrix multiplication. A master server owns two matrices $\mathbf {A}$ and {B}$ hires worker nodes help computing their The should remain information-theoretically from workers. Codes fixed require assign tasks workers then wait a predetermined number finish assigned tasks. size tasks, hence scheme, depends on that waits for. design rateless multiplication called RPM3. In contrast fixed-rate schemes, our scheme fixes allows send multiple keeps sending receiving results until it can decode multiplication; rendering adaptive heterogeneous environments. Despite resulting in smaller than known straggler-tolerant RPM3 provides mean waiting time by leveraging heterogeneity is studied under different models workers’ service time. provide upper lower bounds both models. addition, we worker-dependent model.