Multilevel Coding with a Class of Decomposable Finite-Geometry LDPC Codes

This paper proposes a class of decomposable LDPC codes based on finite geometry EG(m, p
^s
) over bandlimited AWGN channel. These LDPC codes defined as the origin LDPC codes are decomposed into a few small LDPC codes as component codes in multilevel coding. It is shown that the origin LDPC codes demand generic M-ary Min-Sum algorithm while the component codes only require a few binary Min-Sum algorithm implementations in multi-stages decoding. The method proposed simplifies the decoding complexity.