  A generalized low-density parity-check (GLDPC) code is a class of codes,
where single parity check nodes in a conventional low-density parity-check
(LDPC) code are replaced by linear codes with higher parity check constraints.
In this paper, we introduce a new method of constructing GLDPC codes by
inserting the generalized check nodes for partial doping. While the
conventional protograph GLDPC code dopes the protograph check nodes by
replacing them with the generalized check nodes, a new GLDPC code is
constructed by adding the generalized check nodes and partially doping the
selected variable nodes to possess higher degrees of freedom, called a
partially doped GLDPC (PD-GLDPC) code. The proposed PD-GLDPC codes can make it
possible to do more accurate extrinsic information transfer (EXIT) analysis and
the doping granularity can become finer in terms of the protograph than the
conventional GLDPC code. We also propose the constraint for the typical minimum
distance of PD-GLDPC codes and prove that the PD-GLDPC codes satisfying this
condition have the linear minimum distance growth property. Furthermore, we
obtain the threshold optimized protograph for both regular and irregular
ensembles of the proposed PD-GLDPC codes over the binary erasure channel (BEC).
Specifically, we propose the construction algorithms for both regular and
irregular protograph-based PD-GLDPC codes that enable the construction of GLDPC
codes with higher rates than the conventional ones. The block error rate
performance of the proposed PD-GLDPC code shows that it has a reasonably good
waterfall performance with low error floor and outperforms other LDPC codes for
the same code rate, code length, and degree distribution.
