Codes for iterative decoding from partial geometries

This work develops codes suitable for iterative decoding using the sum-product algorithm. We consider regular low-density parity-check (LDPC) codes derived from partial geometries, a large class of combinatorial structures which include several of the previously proposed algebraic constructions for LDPC codes as special cases. We derive bounds on minimum distance and rank₂(H) for codes from partial geometries, and present constructions and performance results for two classes of partial geometries which have not previously been proposed for use with iterative decoding.