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Fundamental Limits of Coded Linear Transform

2018/04/25 by Sinong Wang, Jiashang Liu, Wang, Sinong +5
Computer Science · #Caching and Content Delivery #Cooperative Communication and Network Coding #Distributed #FOS: Computer and information sciences #Information Theory (cs.IT) #Parallel #Stochastic Gradient Optimization Techniques #and Cluster Computing (cs.DC)

paper · pdf · doi:10.48550/arxiv.1804.09791

openalex publication_date 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded computation strategy, referred to as diagonal code, that achieves the optimum recovery threshold and the optimum computation load. This is the first code that simultaneously achieves two-fold optimality in coded distributed linear transforms. Furthermore, by leveraging the idea from random proposal graph theory, we design two random codes that can guarantee optimum recovery threshold with high probability but with much less computation load. These codes provide order-wise improvement over the state-of-the-art. Moreover, the experimental results show significant improvement compared to both uncoded and existing coding schemes.

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