  This paper considers the optimization of multi-edge type low-density
parity-check (METLDPC) codes to maximize the decoding threshold. We propose an
algorithm to jointly optimize the node degree distribution and the multi-edge
structure of MET-LDPC codes for given values of the maximum number of
edge-types and maximum node degrees. This joint optimization is particularly
important for MET-LDPC codes as it is not clear a priori which structures will
be good. Using several examples, we demonstrate that the MET-LDPC codes
designed by the proposed joint optimization algorithm exhibit improved decoding
thresholds compared to previously reported MET-LDPC codes.
