Sub-Linear Overhead in Static Schedules for Fault-Tolerant Transmission

Shared communication media are widely used in many applications including safety critical applications such as control systems on flights or autonomous vehicles. Noise and transient errors can cause transmission failures. We consider the problem of designing fault tolerant static schedules for transmitting messages in these media. In particular, we assume that the schedule of transmission over all messages must be computed in advance and must guarantee that all messages will be delivered as long as the number of medium errors falls below a provided upper bound, regardless of when the medium errors occur. It is crucial that the messages be delivered in a timely manner, and hence we are interested in minimizing the length of the schedule that achieves the desired level of fault tolerance. In this paper, we provide an efficient algorithm for producing a schedule for n messages with total length n + O(f² log² n) that can tolerate f medium errors. We also prove that fault-tolerant schedules with length n+O(f log f log n) exist. Since n steps are required to transmit n messages, the overhead of fault tolerance is characterized by the additive terms of O(f² log² n) and O(f log f log n), respectively. Both of these terms are sublinear in n and represent asymptotic improvements to the previously best known schedule, which has overhead fn/2.