Constructing low-density parity-check codes with circulant matrices

This is a report on the authors' ongoing effort to implement low-density parity-check codes with iterative belief propagation decoding in a communication system. The system requires the codes to have block lengths from 1000 to 2000 bits. We describe two different methods of constructing the codes using: (1) a combination of random and circulant matrices, and (2) random and circulant matrices with constraints to control the number of low weight codewords. We illustrate the performances of the different constructions with simulations.