Asynchronous Agreement and Its Relation with Error-Correcting Codes

  • Authors:

  • Roy Friedman;Achour Mostefaoui;Sergio Rajsbaum;Michel Raynal

  • Affiliations:

  • -;-;-;-

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 2007

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Abstract

The condition-based approach identifies sets of input vectors, called conditions, for which it is possible to design an asynchronous protocol solving a distributed problem despite process crashes. This paper establishes a direct correlation between distributed agreement problems and error-correcting codes. In particular, crash failures in distributed agreement problems correspond to erasure failures in error-correcting codes and Byzantine and value domain faults correspond to corruption errors. This correlation is exemplified by concentrating on two well-known agreement problems, namely, consensus and interactive consistency, in the context of the condition-based approach. Specifically, the paper presents the following results: First, it shows that the conditions that allow interactive consistency to be solved despite f_{c} crashes and f_{e} value domain faults correspond exactly to the set of error-correcting codes capable of recovering from f_{c} erasures and f_{e} corruptions. Second, the paper proves that consensus can be solved despite f_{c} crash failures iff the condition corresponds to a code whose Hamming distance is f_{c} + 1 and Byzantine consensus can be solved despite f_{b} Byzantine faults iff the Hamming distance of the code is 2f_{b} + 1. Finally, the paper uses the above relations to establish several results in distributed agreement that are derived from known results in error-correcting codes and vice versa.