Distributed Matrix Multiplication Based on Frame Quantization for Straggler Mitigation

Abstract

The number of available worker nodes for distributed computing can be limited and varying in wireless networks with noisy channels. However, the conventional straggler mitigation schemes ensure perfect reconstruction only when the number of worker nodes is more than a predetermined number, called the recovery threshold. When the number of worker nodes is less than the recovery threshold, the conventional schemes show a poor reconstruction performance. To facilitate distributed computing in noisy channels, leveraging the tensor product representation and frame quantization theory, we propose a novel straggler mitigation scheme for distributed matrix multiplication. The proposed scheme offers a reasonable reconstruction performance even when the number of worker nodes is varying and limited. By analyzing the computation error, we figure out the conditions required for encoding and decoding frame design, which suggest using uniform tight frames for encoding and their Moore-Penrose inverse for decoding. The superiority of the proposed scheme to the conventional straggler mitigation schemes when the number of available worker nodes is limited is verified by simulations.