  We consider wireless sensor networks secured by the heterogeneous random key
predistribution scheme under an on/off channel model. The heterogeneous random
key predistribution scheme considers the case when the network includes sensor
nodes with varying levels of resources, features, or connectivity requirements;
e.g., regular nodes vs. cluster heads, but does not incorporate the fact that
wireless channel are unreliable. To capture the unreliability of the wireless
medium, we use an on/off channel model; wherein, each wireless channel is
either on (with probability $\alpha$) or off (with probability $1-\alpha$)
independently. We present conditions (in the form of zero-one laws) on how to
scale the parameters of the network model so that with high probability the
network is $k$-connected, i.e., the network remains connected even if any $k-1$
nodes fail or leave the network. We also present numerical results to support
these conditions in the finite-node regime.
