2019 IEEE Information Theory Workshop (ITW) 2019
DOI: 10.1109/itw44776.2019.8989254
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Collaborative Decoding of Polynomial Codes for Distributed Computation

Abstract: 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 nume… Show more

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Cited by 16 publications
(6 citation statements)
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“…Such ideas have also been extended to also provide Byzantine robustness and data privacy. Specifically, the coded computing paradigm has recently emerged by adapting erasure coding ideas to design straggler-resilient, Byzantine-robust and private distributed computing systems often involving polynomial-type computations (Yu et al 2019;Subramaniam, Heidarzadeh, and Narayanan 2019;Tang et al 2021;So, Guler, and Avestimehr 2020;Sohn et al 2020;So et al 2021). However, many applications involve non-polynomial computations as training and inference of neural networks.…”
Section: Related Workmentioning
confidence: 99%
“…Such ideas have also been extended to also provide Byzantine robustness and data privacy. Specifically, the coded computing paradigm has recently emerged by adapting erasure coding ideas to design straggler-resilient, Byzantine-robust and private distributed computing systems often involving polynomial-type computations (Yu et al 2019;Subramaniam, Heidarzadeh, and Narayanan 2019;Tang et al 2021;So, Guler, and Avestimehr 2020;Sohn et al 2020;So et al 2021). However, many applications involve non-polynomial computations as training and inference of neural networks.…”
Section: Related Workmentioning
confidence: 99%
“…In fact, this is a limitation of many other problems such as verifiable computing and machine learning [212], [213]. Recently, several works have extended LCC to the analog domain to address these challenges [210], [211], [214], [215], but they either focus only on straggler-mitigation [215], privacy [210], [211] or Byzantine-robustness [214]. An interesting open problem is to design a framework that jointly tackles these three challenges in the analog domain.…”
Section: Secure Model Aggregation In Federated Learningmentioning
confidence: 99%
“…The master can thus use this fact to alleviate the assumption of limited knowledge of the malicious workers. In [43] and [44] variants of Reed-Solomon codes are used to half the damage of the malicious workers when the workers introduce random noise and when the workers introduce any kind of noise, respectively. The disadvantage of [44] is the high computational complexity incurred by the master.…”
Section: Introductionmentioning
confidence: 99%
“…The ideas used in [50] are similar to the ideas used in this work. However, [28], [41], [43], [44] and [50] consider security in settings where the workers are assumed to have similar resources. In addition, a maximum amount of stragglers is assumed.…”
Section: Introductionmentioning
confidence: 99%