Abstract: Described herein is a method and system that provides a class of error correction codes which can be used in communication systems to correct errors which may be introduced by a communication channel. In particular, a “staircase matrix” or “staircase LDPC code” is defined that enables performance gains associated with nonbinary LDPC codes while requiring low encoding complexity. Also, the concepts, systems and techniques described herein allow for implementation of a single encoder and decoder structure which can realize arbitrary rational coding rates, thus enabling a communication system to easily adapt a coding rate to different coding requirements.