Coding for distributed computing supports lowlatency 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.

Distributed storage systems suffer from significant repair traffic generated due to frequent storage node failures. This paper shows that properly designed low-density parity-check (LDPC) codes can substantially reduce the amount of required block downloads for repair thanks to the sparse nature of their factor graph representation. In particular, with a careful construction of the factor graph, both low repair-bandwidth and high reliability can be achieved for a given code rate. First, a formula for the average repair bandwidth of LDPC codes is developed. This formula is then used to establish that the minimum repair bandwidth can be achieved by forcing a regular check node degree in the factor graph.Moreover, it is shown that given a fixed code rate, the variable node degree should also be regular to yield minimum repair bandwidth, under some reasonable minimum variable node degree constraint.It is also shown that for a given repair-bandwidth requirement, LDPC codes can yield substantially higher reliability than currently utilized Reed-Solomon (RS) codes. Our reliability analysis is based on a formulation of the general equation for the mean-time-to-data-loss (MTTDL) associated with LDPC codes. The formulation reveals that the stopping number is closely related to the MTTDL. It is further shown that LDPC codes can be designed such that a small loss of repair-bandwidth optimality may be traded for a large improvement in erasure-correction capability and thus the MTTDL. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

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Recently, coding has been a useful technique to mitigate the effect of stragglers in distributed computing.However, coding in this context has been mainly explored under the assumption of homogeneous workers, although the real-world computing clusters can be often composed of heterogeneous workers that have different computing capabilities. The uniform load allocation without the awareness of heterogeneity possibly causes a significant loss in latency. In this paper, we suggest the optimal load allocation for coded distributed computing with heterogeneous workers. Specifically, we focus on the scenario that there exist workers having the same computing capability, which can be regarded as a group for analysis. We rely on the lower bound on the expected latency and obtain the optimal load allocation by showing that our proposed load allocation achieves the minimum of the lower bound for a sufficiently large number of workers. From numerical simulations, when assuming the group heterogeneity, our load allocation reduces the expected latency by orders of magnitude over the existing load allocation scheme.

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