Partially Quasi-Cyclic Protograph-Based LDPC Codes

A significant amount of the analysis of protograph-based Low-Density Parity-Check (LDPC) codes has been devoted to the subclass of Quasi-Cyclic (QC) LDPC codes. Despite their implementation advantages and algebraic properties that make them easy to analyze, protograph-based QC-LDPC codes have undesirable fixed upper limits on important code parameters. This implies that picking a QC code from an asymptotically good or capacity approaching ensemble is suboptimal, since long QC codes will not perform close to the ensemble asymptotic limits.