Coded Distributed Computing for Resilient, Secure and Private Matrix-Vector Multiplication in Edge-Enabled Metaverse

Metaverse is an immersive and photorealistic shared virtual world that requires efficient rendering and processing of millions of virtual objects and scenes. This leads to the requirements of computing time-sensitive and computation-intensive tasks, primarily focused on matrix multiplication. Cloud computing can be leveraged to process computation-intensive tasks. However, it is not able to meet the ultra-low latency requirements of immersive experiences due to the remote servers. In this paper, we propose an effectively distributed edge computing framework to compute high-dimensional matrix multiplication for the Metaverse. With the distributed edge computing, the high-dimensional matrix multiplication task is divided into multiple smaller subtasks, which are then assigned to nearby edge servers (workers). However, leveraging distributed edge servers raises emerging issues due to the existence of stragglers, malicious, and colluding servers, which limits the applications of distributed edge computing in the Metaverse system. Thus, we design a resilient, secure, and private coded distributed computing (RSPCDC) scheme to jointly address the aforementioned issues. Firstly, the RSPCDC scheme reduces overall computation latency by lowering the recovery threshold. Secondly, to identify malicious (e.g., Byzantine) workers, a verification approach is embedded in the scheme to promptly detect the Byzantine attack without requiring additional workers. Thirdly, the RSPCDC scheme provides (information-theoretic) privacy protection for the input data against the collusion of workers. Fourthly, the results of subtasks computed by stragglers are fully utilized to enhance the computation performance during the recovery of the final result. In addition, the RSPCDC scheme is designed and deployed in practical scenarios in which the computing resources of the workers are heterogeneous. Extensive performance evaluations are provided to demonstrate the improvement and effectiveness of the proposed RSPCDC scheme in comparison to existing schemes.