  A class of doubly-generalized low-density parity-check (D-GLDPC) codes, where
single parity-check (SPC) codes are used as variable nodes (VNs), is
investigated. An expression for the growth rate of the weight distribution of
any D-GLDPC ensemble with a uniform check node (CN) set is presented at first,
together with an analytical technique for its efficient evaluation. These tools
are then used for detailed analysis of a case study, namely, a rate-1/2 D-GLDPC
ensemble where all the CNs are (7,4) Hamming codes and all the VNs are length-7
SPC codes. It is illustrated how the VN representations can heavily affect the
code properties and how different VN representations can be combined within the
same graph to enhance some of the code parameters. The analysis is conducted
over the binary erasure channel. Interesting features of the new codes include
the capability of achieving a good compromise between waterfall and error floor
performance while preserving graphical regularity, and values of threshold
outperforming LDPC counterparts.
