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Coded computing has proved to be useful in distributed computing. We haveobserved that almost all coded computing systems studied so far consider asetup of one master and some workers. However, recently emerging technologiessuch as blockchain, internet of things, and federated learning introduce newrequirements for coded computing systems. In these systems, data is generatedin a distributed manner, so central encoding/decoding by a master is notfeasible and scalable. This paper presents a fully distributed coded computingsystem that consists of $k\in\mathbb{N}$ data owners and $N\in\mathbb{N}$workers, where data owners employ workers to do some computations on theirdata, as specified by a target function $f$ of degree $d\in\mathbb{N}$. Asthere is no central encoder, workers perform encoding themselves, prior tocomputation phase. The challenge in this system is the presence of adversarialdata owners that do not know the data of honest data owners but causediscrepancies by sending different data to different workers, which isdetrimental to local encodings in workers. There are at most$\beta\in\mathbb{N}$ adversarial data owners, and each sends at most$v\in\mathbb{N}$ different versions of data. Since the adversaries and theirpossibly colluded behavior are not known to workers and honest data owners,workers compute tags of their received data, in addition to their maincomputational task, and send them to data owners to help them in decoding. Weintroduce a tag function that allows data owners to partition workers into setsthat previously had received the same data from all data owners. Then, wecharacterize the fundamental limit of the system, $t^*$, which is the minimumnumber of workers whose work can be used to correctly calculate the desiredfunction of data of honest data owners. We show that $t^*=v^{\beta}d(K-1)+1$,and present converse and achievable proofs.

Vers: fully distributed Coded Computing System with Distributed Encoding