Study on short loops structure in LDPC-like sparse bipartite graphs based on graph kernel

Abstract

Low-Density Parity-Check (LDPC) codes are widely used in communication systems for their ability to provide efficient and effective error correction. LDPC codes are based on sparse bipartite graphs, which are known to exhibit short cycles or loops that can affect their performance. In this report, I will investigate the structure of short loops in LDPC-like sparse bipartite graphs using graph kernel methods. Specifically, we develop a graph kernel based on the Weisfeiler-Lehman algorithm to measure the similarity of graphs with different short loop structures. I then try applying this kernel to a set of LDPC-like sparse bipartite graphs with varying degrees of short loops and analyze the resulting similarity scores. Overall, our study contributes to a deeper understanding of the structure of LDPC-like sparse bipartite graphs and their role in the performance of LDPC codes.