Design of fully-source-involved LDPC codes with tripartite graph

In this paper we consider a class of fully-source-involved low-density parity-check (FSI-LDPC) codes. We show that the code designed based on the conventional bipartite graph may not be feasible or implementable. We investigate the applicability of the bipartite graph as a representation of an FSI-LDPC code for density evolution. We discuss the applicable range of the bipartite representation. Then we introduce tripartite graph for FSI-LDPC codes as a modification of the conventional bipartite representation. In this graph, we consider the degree distributions for source nodes and redundancy nodes separately. For design of FSI-LDPC codes, we show that, when code rate is low, possible performance degradation originated from the conventional bipartite representation can be prevented by adopting the tripartite representation.