Design of multi-edge type bilayer-expurgated LDPC codes

This paper presents a new bilayer-expurgated LDPC (BE-LDPC) code design for decode-and-forward relay system. The code design is based on the multi-edge type LDPC (MET-LDPC) code structure. The lower and upper graphs´ edges of the BE-LDPC codes are represented via different edge types. We call the codes as multi-edge type bilayer-expurgated LDPC (MET-BE-LDPC) codes. We derive the relationship between the lower and the overall graphs of the MET-BE-LDPC codes using the multi-edge type multinomials. This relationship acts as a constraint in optimizing the MET-BE-LDPC codes under the density evolution. We apply the differential evolution algorithm to search for the best MET-BE-LDPC codes. Applying the proposed methodology, two MET-BE-LDPC codes are designed. The codes perform asymptotically within 0.08474-0.5087 dB from the theoretical limits. Finally, we demonstrate that the proposed methodology can be used to design the BE-LDPC codes at a larger source-to-relay and source-to-destination SNR differences.