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Distributed Encoding System in the Presence of Adversarial Sources

Abadi Khooshemehr, Nastaran | 2023

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 56569 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Maddah Ali, Mohammad Ali
  7. Abstract:
  8. In communications systems, coding is used to combat channel errors. The redundancy introduced by coding enables the detection and/or correction of errors occurring in the channel. In addition to communications systems, coding is also beneficial in various other systems such as distributed storage systems and blockchain systems to cope with node failures, data erasures, and adversarial behaviors attempting to modify information. In existing applications of coding, it is generally assumed that the encoding operation is performed correctly and without errors, and errors are applied to the encoded data. In recent years, applications have emerged where the assumption of error-free encoding is not always true. For instance, in distributed systems like blockchain and the Internet of Things, data generation has a distributed nature, and data is generated by multiple distributed sources. With distributed encoding model, the phenomenon of errors in encoding is introduced. In this thesis, after reviewing some classical coding results and applications of coding in distributed systems including message transmission networks, distributed storage systems, and sensor networks, we introduce and study two new systems named Distributed Encoding System and Distributed Coded Computing System. These systems serve as good models for emerging decentralized systems such as blockchain and the Internet of Things. In the Distributed Encoding System, we have a number of data sources and storage nodes. Sources send their data to storage nodes, which store the received data in an encoded form. In this system, some of the sources may be compromised by an attacker and send different data to different storage nodes, disrupting the encoding process in these nodes and which leads to error propagation. We define the fundamental limit of the Distributed Encoding System as the minimum number of storage nodes required to correctly recover the data of honest sources from any number of those storage nodes. We obtain this fundamental limit by providing achievable and converse proofs when linear codes are used. The Distributed Coded Computing System consists of a number of data sources and workers. Data sources use distributed encoding to distribute their data among the workers for computing a target function of their data. Sources send their data to the workers, who first encode the received data using Lagrange coding and then compute the target function from the encoded data. Sources can obtain their target function from the results of the workers. Similar to the attacker model in the Distributed Encoding System, in this system, there are also some compromised sources that send different data to different workers, causing disruption in their encoding and computations. Due to the presence of the attacker, workers calculate a label of the received data in addition to computing the target function from the encoded data, and they send it back to the sources. We define the fundamental limit of the Distributed Coded Computing System as the minimum number of workers required to correctly recover the target function of the honest sources from any number of workers. After finding a proper tag function, we obtain this fundamental limit by providing achievable and converse proofs
  9. Keywords:
  10. Coding Theory ; Blockchain ; Distributed System ; Active Adversary ; Coded Computing ; Communication System

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