We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous distributed protocol while tolerating an optimal corruption of a @math fraction of all messages while incurring a moderate blowup of @math in the communication complexity. Our result is the first fully distributed interactive coding scheme in which the topology of the communication network is not known in advance. Prior work required either a coordinating node to be connected to all other nodes in the network or assumed a synchronous network in which all nodes already know the complete topology of the network.
@cite_21: In this paper we study the problem of achieving Byzantine agreement among a set of processors, where the processors are computationally sound but their interfaces with the communication channels may be faulty. We consider three types of fault, namely message corruption, message loss, and spurious message generation. We present the following results for this model: (i) If all three types of faults are present then the problem is equivalent to the classical Byzantine generals problem. (ii) In the cases where only message corruption can occur, agreement becomes trivial and can be achieved in one round. (iii) If spurious message generation is ruled out, that is, when interfaces may fault only when sensitized, agreement is possible irrespective of the ratio of the number of processors having faulty interfaces with the total number of processors.
@cite_19: 
@cite_10: We consider agreement and leader election on asynchronous complete networks when the processors are reliable, but some of the channels are subject to failure. Fischer, Lynch, and Paterson have already shown that no deterministic algorithm can solve the agreement problem on asynchronous networks if any processor fails during the execution of the algorithm. Therefore, we consider only channel failures. The type of channel failure we consider in this paper is Byzantine failure, that is, channels fail by altering messages, sending false information, forging messages, losing messages at will, and so on. There are no restrictions on the behavior of a faulty channel. Therefore, a faulty channel may act as an adversary who forges messages on purpose to prevent the successful completion of the algorithm. Because we assume an asynchronous network, the channel delays are arbitrary. Thus, the faulty channels may not be detectable unless, for example, the faulty channels cause garbage to be sent. We present the first known agreement and leader election algorithm for asynchronous complete networks in which the processors are reliable but some channels may be Byzantine faulty. The algorithm can tolerate up to ⌊n-2 2⌋ faulty channels, where n is the number of processors in the network. We show that the bound on the number of faulty channels is optimal. When the processors terminate their corresponding algorithms, all the processors in the network will have the same correct vector, where the vector contains the private values of all the processors.
@cite_12: We study the problem of leader election in the presence of intermittent link failures. We assume that up to N 2-1 links incident on each node may fail during the execution of the protocol. We present a message optimal algorithm with message complexity O(N sup 2 ).
@cite_20: In early stage, the Byzantine agreement (BA) problem was studied with single faults on processors in either a fully connected network or a nonfully connected network. Subsequently, the single fault assumption was extended to mixed faults (also referred to as hybrid fault model) on processors. For the case of both processor and link failures, the problem has been examined in a fully connected network with a single faulty type, namely an arbitrary fault. To release the limitations of a fully connected network and a single faulty type, the problem is reconsidered in a general network. The processors and links in such a network can both be subjected to different types of fault simultaneously. The proposed protocol uses the minimum number of message exchanges and can tolerate the maximum number of allowable faulty components to make each fault-free processor reach an agreement.
Previous work in distributed settings that allow edge failures are typically different from our setting in various aspects. Most notable are synchrony assumptions, complete communication graphs, addressing specific distributed tasks and assuming a bound on the number of links that may exhibit failures. This is in contrast to our work, which addresses an asynchronous setting with an arbitrary topology, and considers the simulation of any distributed task. In particular, all links may send corrupted messages, with the bound being the number of corruptions rather than the number of faulty links. For instance, Singh @cite_12 and Sayeed, Abu-Amara and Abu-Amara @cite_10 consider the specific task of leader election and agreement for complete networks. Gong, Lincoln, and Rushby @cite_19 , Siu, Chin and Yang @cite_20 and Dasgupta @cite_21 consider agreement in complete synchronous networks with both faulty nodes and faulty links.