Design of rate-compatible protograph-based LDPC codes with mixed circulants

We propose a novel design of rate-compatible protograph-based low-density parity-check code families that can cover a wide range of code rates. In contrast to traditional method of lifting, our lifting method use a combination of different circulant matrix sizes for the base protograph and accumulator to increase the number of achievable rates. We apply this method to an existing code family called AR4JA, which can offer variable rates of R = n+1/n+2 by process of extension. The proposed codes namely mixed-circulant rate-compatible protograph code (MCRC-PC) can reduce the rate step within the AR4JA family. We show that the proposed codes can also retain many of the favorable properties of protograph codes such as a fast encoder and decoder implementation. A set of length k=1024 MCRC-PC codes is designed with decoding thresholds obtained from multi-edge type density evolution, and simulation results show that the rate compatible code family can achieve good performance under message passing decoding algorithm.