Spatially-coupled irregular LDPC codes by non-square superposition matrices

Spatially-coupled irregular LDPC codes by non-square superposition matrices are proposed. Starting with a binary base matrix and replacing non-zero entries in the base matrix by superposition matrices produces a parity-check matrix and its corresponding code ensemble. The proposed codes have two features: a) flexible code rates because the size of the superposition matrix is arbitrarily adjusted, and b) guaranteed iterative decoding performance because the degree distributions of the superposition matrix are optimized, even in a finite coupling width. The numerical analysis of density evolution and Monte-Carlo simulations show that our proposed code ensembles approach the Shannon limits at arbitrary code rates and outperform the conventional codes.