Performance of bilayer-lengthened LDPC codes under joint decoding

This paper presents an LDPC code design for decode-and-forward (DF) relay systems. Our design is based on the graphical family of the bilayer-lengthened LDPC codes (BL-LDPC) when joint decoding is performed over the overall expanded graph. To design the BL-LDPC codes under joint decoding, we use the framework of the multi-edge type LDPC (MET-LDPC) codes to represent and optimize the codes. The optimum overall expanded graph of the BL-LDPC codes is found using differential evolution. We demonstrate that a properly designed expanded BL-LDPC code performs asymptotically within 0.1222 dB and 0.10775 dB from the theoretical limits.