  Due to process variation in nanoscale manufacturing, there may be permanently
missing connections in information processing hardware. Due to timing errors in
circuits, there may be missed messages in intra-chip communications, equivalent
to transiently missing connections. In this work, we investigate the
performance of message-passing LDPC decoders in the presence of missing
connections. We prove concentration and convergence theorems that validate the
use of density evolution performance analysis. Arbitrarily small error
probability is not possible with missing connections, but we find suitably
defined decoding thresholds for communication systems with binary erasure
channels under peeling decoding, as well as binary symmetric channels under
Gallager A and B decoding. We see that decoding is robust to missing wires, as
decoding thresholds degrade smoothly. Moreover, there is a stochastic
facilitation effect in Gallager B decoders with missing connections. We also
compare the decoding sensitivity with respect to channel noise and missing
wiring.
