Fault tolerance in a class of sorting networks

The early study of fault tolerance in efficient sorting networks only achieved single-fault tolerance. By eliminating critical comparators, L. Rudolph (1985) presented a 1-fault tolerant design of the balanced sorting network (BSN) at the cost of one redundant stage of N/2 comparators and two permuters external to the network. In this paper, we show, however, that 1-fault tolerance of BSN can be achieved without introducing redundancy and external permuters. Furthermore, we provide solutions to the open question of how to achieve multiple-fault tolerance in BSN. We analyze the problem from a higher-level by introducing a new concept of critical stages, and find that all stages in previous designs are critical. A 2-fault tolerant design of BSN is then discovered after eliminating its critical stages. The new design has a similar network architecture (i.e., a multistage network with the output recirculated back to the input) and the same hardware cost as Rudolph´s, but it has many distinguished features. The performance analysis shows that the new designs achieve much higher probabilities of correct sorting in the presence of faulty comparators than the previous reported designs