Low-Rate Non-Binary LDPC Codes for Coherent and Blockwise Non-Coherent AWGN Channels

Low-rate non-binary low-density parity-check (LDPC) codes for coherent and blockwise non-coherent additive white Gaussian noise (AWGN) channels are developed. The proposed construction is based on the concatenation of non-binary outer LDPC codes with inner binary codes. In case the binary codes are chosen to be Hadamard or Reed-Muller (RM) codes, the complexity of the decoding scheme is considerably reduced. An asymptotic analysis of the concatenation with help of composite capacity considerations and density evolution (DE) is provided, from which guidelines on the choice of both inner and outer codes are devised. Finite length designs presented in this work confirm the excellent performance of the proposed codes.