Design of Generalized LDPC codes and their decoders
Shadi Abu‐Surra, W.E. Ryan, Gianluigi Liva · elib (German Aerospace Center) · 2007
Abstract — We first consider the design of generalized LPDC (G-LDPC) codes with recursive systematic convolutional (RSC) constraint nodes in place of the standard single parity check constraint nodes. Because rate-1/2 RSC nodes lead to low-rate G-LDPC codes, we consider high-rate tail-biting RSC nodes for which Riedel’s APP-decoder based on the reciprocal-dual code trellis becomes necessary. We present the log-domain version of this decoder as well as a suboptimal approximation. Another approach to increasing the rate of G-LDPC codes is via the class of doubly generalized LDPC (DG-LDPC) codes. We show how the graph of a DG-LDPC code (called a DG-graph) may be transformed into a G-graph. This alternative representation of DG-LDPC codes leads to a modified-schedule G-graph decoder which is equivalent to the flooding-schedule DG-graph decoder. Lastly, we demonstrate the unequal error protection capability of selected G-LDPC codes. Our codes are based on protographs and most of them have adjacency matrices in block-circulant form and, hence, are quasi-cyclic. I.