# Block-Diagonal and LT Codes for Distributed Computing With Straggling Servers

arXiv: https://arxiv.org/abs/1712.08230 · HTML: https://mlsanity.com/paper/1712.08230/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2017.

## Built on by (most cited first, 5 of 5)

- [CodedPaddedFL and CodedSecAgg: Straggler Mitigation and Secure Aggregation in Federated Learning](https://mlsanity.com/paper/2112.08909/) (2021)
- [Coding for Straggler Mitigation in Federated Learning](https://mlsanity.com/paper/2109.15226/) (2021)
- [Straggler-Resilient Differentially-Private Decentralized Learning](https://mlsanity.com/paper/2212.03080/) (2022)
- [Randomized Polar Codes for Anytime Distributed Machine Learning](https://mlsanity.com/paper/2309.00682/) (2023)
- [Nested Gradient Codes for Straggler Mitigation in Distributed Machine Learning](https://mlsanity.com/paper/2212.08580/) (2022)

## Abstract (arXiv)

We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to each submatrix. For this scheme, we prove that up to a given number of partitions the communication load and the computational delay (not including the encoding and decoding delay) are identical to those of the scheme recently proposed by Li et al., based on a single, long MDS code. However, due to the use of shorter MDS codes, our scheme yields a significantly lower overall computational delay when the delay incurred by encoding and decoding is also considered. We further propose a second coded scheme based on Luby Transform (LT) codes under inactivation decoding. Interestingly, LT codes may reduce the delay over the partitioned scheme at the expense of an increased communication load. We also consider distributed computing under a deadline and show numerically that the proposed schemes outperform other schemes in the literature, with the LT code-based scheme yielding the best performance for the scenarios considered.