Spectral Shape of Non-Binary LDPC Code Ensembles with Separated Variable Nodes

The non-binary weight distribution and its spectral shape is developed for a partially-structured ensemble of low-density parity-check codes over finite fields. The ensemble is characterized by all degree-2 variable nodes and some of the degree-3 variable nodes being separated. It is shown that, under node separation, the typical minimum distance is strictly positive and significantly higher than the one of the corresponding unstructured ensemble