Hierarchical Coding for Distributed Computing

Coding for distributed computing supports low-latency computation by relieving the burden of straggling workers. While most existing works assume a simple master-worker model, we consider a hierarchical computational structure consisting of groups of workers, motivated by the need to reflect the architectures of real-world distributed computing systems. In this work, we propose a hierarchical coding scheme for this model, as well as analyze its decoding cost and expected computation time. Specifically, we first provide upper and lower bounds on the expected computing time of the proposed scheme. We also show that our scheme enables efficient parallel decoding, thus reducing decoding costs by orders of magnitude over non-hierarchical schemes. When considering both decoding cost and computing time, the proposed hierarchical coding is shown to outperform existing schemes in many practical scenarios.Comment: 7 pages, part of the paper is submitted to ISIT201

GCSA Codes with Noise Alignment for Secure Coded Multi-Party Batch Matrix Multiplication

A secure multi-party batch matrix multiplication problem (SMBMM) is considered, where the goal is to allow a master to efficiently compute the pairwise products of two batches of massive matrices, by distributing the computation across S servers. Any X colluding servers gain no information about the input, and the master gains no additional information about the input beyond the product. A solution called Generalized Cross Subspace Alignment codes with Noise Alignment (GCSA-NA) is proposed in this work, based on cross-subspace alignment codes. The state of art solution to SMBMM is a coding scheme called polynomial sharing (PS) that was proposed by Nodehi and Maddah-Ali. GCSA-NA outperforms PS codes in several key aspects - more efficient and secure inter-server communication, lower latency, flexible inter-server network topology, efficient batch processing, and tolerance to stragglers. The idea of noise alignment can also be combined with N-source Cross Subspace Alignment (N-CSA) codes and fast matrix multiplication algorithms like Strassen's construction. Moreover, noise alignment can be applied to symmetric secure private information retrieval to achieve the asymptotic capacity