Strongly Connected Ramanujan Graphs for Highly Symmetric LDPC Codes

A number of studies focus on Low-Density Parity-Check (LDPC) codes to ensure reliable data communications. This study proposes an algebraic algorithm to generate strongly connected Ramanujan graphs able to provide highly symmetric LDPC codes with minimized error floor. Several Ramanujan graphs are created using GAP system software to generate a rank-efficient parity-check matrix with fixed-rate LDPC codes. We find that Ramanujan LDPC codes achieve frame error rate and bit error rate on the order of 10 - 5 and 10 - 6 , respectively. Furthermore, the codes outperform QC LDPC codes and those Ramanujan LDPC codes in literature.