The Cycle-Concentrating PEG Algorithm for Protograph Generalized LDPC Codes

In this paper, we propose the cycle-concentrating progressive edge growth (CC-PEG) algorithm for lifting protograph generalized low-density parity-check (GLDPC) codes. In GLDPC codes,
undoped variable nodes
(VNs) that are not connected to generalized constraint (GC) nodes are more vulnerable to channel errors than
doped VNs
protected by GC nodes. We observe that among GLDPC codes sharing the same protograph structure, codes with fewer local cycles at undoped VNs have better decoding performances. Inspired by this observation, the CC-PEG algorithm is proposed to concentrate local cycles at doped VNs and avoid local cycles at vulnerable undoped VNs during the lifting process. Specifically, the CC-PEG algorithm first collects edges that result in the maximum
undoped girth
, defined as the length of the shortest cycle containing undoped VNs. Following this, the CC-PEG algorithm selects the edge with the lowest
concentrated cycle metric
. Consequently, the lifted codes exhibit asymmetric cycle distributions concentrated around robust doped VNs. Simulation results for various protographs show that the CC-PEG algorithm achieves a performance gain of up to 20 times lower frame error rate compared to conventional lifting algorithms.