A Family of Binary Locally Repairable Codes for Coded Distributed Computing

One of the main bottlenecks in distributed computing systems is the stragglers' problem. Error correction codes have been proposed to alleviate this problem at the cost of coding complexity for the master node. In this work, we aim to reduce this coding complexity and propose a novel family of binary locally repairable codes (BLRC) to encode the distributed tasks in a linear matrix-vector multiplication problem. In comparison to the widely used maximum distance separable (MDS) codes, our proposed codes (i) eliminate the costly multiplication operations from the encoding and decoding processes, (ii) allow for low-complexity recovery within the local groups. We analyze the complexity of our proposed codes and through simulations show that compared to MDS codes, our codes reduce the overall encoding plus computation plus decoding time by more than 35% in many practical scenarios.