Year: 2025
Type: conference-paper
Abstract: Gradient coding enables a user node to efficiently aggregate gradients computed by server nodes from local datasets, achieving low communication costs while ensuring resilience against straggling servers. This paper considers the secure gradient coding problem, where a user aims to compute the sum of the gradients from K datasets with the assistance of$N$distributed servers. The user is required to recover the sum of gradients from the transmissions of any$\mathrm{N}_{\mathrm{r}}$servers, with each dataset assigned to$N-N_{r}+m$servers. The security constraint guarantees that even if the user receives transmissions from all servers, no additional information about the datasets can be obtained beyond the sum of gradients. It has been shown in the literature that the security constraint does not increase the optimal communication cost of the gradient coding problem, provided that enough source keys are shared among the servers. However, the minimum required source key size to ensure security while achieving the optimal communication cost has been studied only for the case$m=1$. In this paper, we focus on the more general case$m \geq 1$and aim to characterize the minimum required source key size for this purpose. A new information-theoretic converse bound on the source key size and a novel achievable scheme with smartly designed assignments are proposed. Our proposed scheme outperforms the optimal scheme based on the widely used cyclic data assignment and coincides with the converse bound under specific system parameters.
Authors: Yang Zhou, Wenbo Huang, Kai Wan, Robert Caiming Qiu
Institution: Huazhong University of Science and Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G2488712091
OpenAlex ID: W4415367515