Classes of LDPC codes constructed from elements of finite fields and cyclotomic cosets

Abstract

In this paper, we derive two algebraic methods for constructing regular low density parity check (LDPC) codes - one based on elements of finite fields and the other directly based on cyclotomic cosets. We show that the constructed codes have high rates and are free of cycles of length four; consequently, they can be decoded using standard iterative decoding algorithms. In addition we compute the exact dimension and establish bounds on the minimum and stopping distances of the constructed codes.