Asynchronous Agreement and Its Relation with Error-Correcting Codes

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 c value domain faults correspond exactly to the set of error-correcting codes capable of recovering from f c erasures and f c corruptions. Second, the paper proves that consensus can be solved despite f c crash failures if the condition corresponds to a code whose Hamming distance is f c + 1 and Byzantine consensus can be solved despite f b Byzantine faults if the Hamming distance of the code is 2 f 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.