Partially-regular LDPC codes with linear encoding complexity and improved thresholds

We consider an ensemble of systematic low-density parity-check (LDPC) codes of length N with linear encoding complexity, i.e., with complexity O(N). We call these codes partially-regular, since they can be considered as modifications of regular LDPC codes. Further, their iterative decoding thresholds on the binary erasure channel (BEC) are found to be significantly better than the thresholds of the corresponding regular LDPC codes.