In this work, we perform an asymptotic analysis of regular LDPC codes when the
decoder is built exclusively out of faulty computing devices. We first look at
the Gallager-B decoding algorithm and determine the impact of the decoder
faultiness on the channel threshold of the code. We also show the existence of a
threshold in terms of the decoder faultiness. We then introduce an extension to
the Gallager-B algorithm that allows trading fault tolerance for decoding
complexity by repeating some messages, and we show how the message repetitions
can be scheduled optimally.  Despite the method's simplicity, optimally
scheduled repetitions can provide large gains in fault tolerance for a small
decoding complexity overhead.