The Effect of PEG-Lifting Order on the Performance of Protograph GLDPC Codes

Generalized low density parity check (GLDPC) codes can be constructed by replacing some single parity check (SPC) nodes in LDPC codes with generalized constraint (GC) nodes. GC nodes are defined by component codes whose minimum distance is larger than that of SPC nodes. Therefore, the variable nodes (VNs) connected to GC nodes, which are called doped VNs, are more protected than the undoped VNs. Due to this effect, we observe that the doped VNs are more robust to local cycles. The distribution of local cycles is affected by the processing VN order of the progressive edge growth (PEG) algorithm, where the latter processed (lifted) VNs tend to have more local cycles. Based on the property of doped VNs and the PEG algorithm, we show that a tangible performance gain is achieved by placing the doped VNs in the latter order of the PEG algorithm compared to the former order. The performance gain is shown with a well known GLDPC code in the literature and over both the binary erasure channel and addictive white Gaussian noise channel.