Efficient Static Schedules for Fault-Tolerant Transmissions on Shared Media

Shared communication media are widely used in many applications including safety-critical applications. However, noise and transient errors can cause transmission failures. We consider the problem of designing and minimizing the length of fault-tolerant static schedules for transmitting messages in these media provided the number of errors fall below some upper bound. To transmit n messages in a medium while tolerating a maximum of f faults, prior work had shown how to construct schedules which had a fault tolerance overhead of $nf/2$. In this paper, we provide an efficient constructive algorithm for producing a schedule for n messages with total length $n\,+\,O(f^{2}\,\mathbf{\log}^{2}\,n)$ that can tolerate f medium errors. We also provide an algorithm for randomly generating fault-tolerant schedules with length $n\,+\,O(f\,\mathbf{\log}(f)\mathbf{\log}(n))$ as well as a technique for quickly verifying these on reasonably small inputs.