Computation Efficient Coded Linear Transform

In large-scale distributed linear transform problems, coded computation plays an important role to reduce the delay caused by slow machines. However, existing coded schemes could end up destroying the significant sparsity that exists in large-scale machine learning problems, and in turn increase the computational delay. In this paper, we propose a coded computation strategy, referred to as diagonal code, that achieves the optimum recovery threshold and the optimum computation load. Furthermore, by leveraging the ideas from random proposal graph theory, we design a random code that achieves a constant computation load, which significantly outperforms the existing best known result. We apply our schemes to the distributed gradient descent problem and demonstrate the advantage of the approach over current fastest coded schemes.