Improved bilayer LDPC codes using irregular check node degree distribution

This paper presents an improved LDPC code design for decode-and-forward relay system. Our design is based on the recent work of bilayer LDPC code structures. We introduce an irregular check node degree distribution for the lower and hyper (overall) bilayer LDPC code Tanner graphs. We derive the exact relationship between the lower and hyper graphs in terms of degree distributions (node perspective). This relationship acts as constraint to perform the density evolution. We apply the differential evolution algorithm to search for the best degree distribution for both bilayer- lengthened and bilayer-expurgated LDPC codes. We show that the performance gap of the codes is within 0.07595 dB and 0.28407 dB from the theoretical limits.