  In this paper, we investigate the error floors of non-binary low-density
parity-check (LDPC) codes transmitted over the memoryless binary-input
output-symmetric (MBIOS) channels. We provide a necessary and sufficient
condition for successful decoding of zigzag cycle codes over the MBIOS channel
by the belief propagation decoder. We consider an expurgated ensemble of
non-binary LDPC codes by using the above necessary and sufficient condition,
and hence exhibit lower error floors. Finally, we show lower bounds of the
error floors for the expurgated LDPC code ensembles over the MBIOS channel.
