  Low-density parity-check (LDPC) codes are specified by graphs, and are the
error correction technique of choice in many communications and data storage
contexts. Message passing decoders diffuse information carried by parity bits
into the payload, and this paper measures the value of engineering parity bits
to be more reliable than message bits. We consider the binary symmetric channel
(BSC) and measure the impact of unequal data protection on the threshold of a
regular LDPC code. Our analysis also includes doping where the parity bits are
known to the decoder. We investigate BSC with Gallager-A decoder, with a
$3$-level-alphabet decoder, and with a full belief propagation decoder. We
demonstrate through theoretical analysis and simulation that non-equiprobable
inputs lead to significant improvements both in the threshold and in the speed
with which the decoder converges. We also show that all these improvements are
possible even with a simple $3$-level-alphabet decoder.
