Cayley Graphs with Large Girth and Constructions of LDPC Codes
Talk by Luana Kurmann
Date: 18.12.24 Time: 16.15 - 17.00 Room: Y27H28
In this talk, we investigate a particular family of graphs with large girth and look at their applications to low-density parity-check (LDPC) codes. Specifically, we study a family of Cayley graphs with large girth over finite fields with prime order, constructed by Margulis. We analyse Margulis' lower bound for the girth of these graphs and compute the exact girth for several prime numbers. Our results show that the actual girth exceeds the bound by an average of about 87% in all cases studied. We show an improvement to Margulis' bound which leads to an average error rate of about 56%. Additionally, we present further observations which suggest that an even better bound may still exist. Furthermore, we show how LDPC codes can be constructed based on these graphs and simulate their error correction performance over an additive white Gaussian noise channel.