Error floors and finite geometries

The structure of certain subgraphs of the Tanner graph of an LDPC code, the trapping sets, has been identified as important for the error floor performance of iterative decoding algorithms. To investigate such sets requires the parity check matrix of the code to be generated with sufficient structure that allows useful information to be obtained while giving good codes. Structures that have been considered include combinatorial designs and classical finite geometries. More recently other finite geometric notions such as partial geometries and generalized d-gons have been considered with some success. This work considers aspects of this approach.