# Collaborative Decoding of Polynomial Codes for Distributed Computation

arXiv: https://arxiv.org/abs/1905.13685 · HTML: https://mlsanity.com/paper/1905.13685/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2019.

## Built on by (most cited first, 3 of 3)

- [ApproxIFER: A Model-Agnostic Approach to Resilient and Robust Prediction Serving Systems](https://mlsanity.com/paper/2109.09868/) (2021)
- [List-Decodable Coded Computing: Breaking the Adversarial Toleration Barrier](https://mlsanity.com/paper/2101.11653/) (2021)
- [Adaptive Verifiable Coded Computing: Towards Fast, Secure and Private Distributed Machine Learning](https://mlsanity.com/paper/2107.12958/) (2021)

## Abstract (arXiv)

We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where t worker nodes return erroneous values. For an additive random Gaussian error model, we show that for all t < N-K, errors can be corrected with probability 1. Further, numerical results show that in the presence of additive errors, when L Reed-Solomon codes are collaboratively decoded, the numerical stability in recovering the error locator polynomial improves with increasing L.