Power- and Bandwidth-Efficient Euclidean Code with Sparse Generator Matrix

In this paper we propose a coded modulation scheme which is defined by a sparse real-valued generator matrix. As forward error correction (FEC) codes directly constructed in the Euclidean space, this kind of Euclidean codes (EC) named G-LDGM (Generalized Low-Density Generator Matrix) codes can naturally match the continuous communication channels. A shaping method based on hypercube lattice is introduced to prevent the power of signals from being too large. A linear-time parametric belief propagation (BP) decoding algorithm is formulated. To reduce the complexity of the decoding algorithm, passing messages are approximated as Gaussian distributions. A simplified analysis is given to show that under certain condition exponential convergence of decoding can be realized. A Monte Carlo density evolution method is provided to optimize the generator matrix. Simulation results suggest that the proposed 10,000 dimension G-LDGM code with no redundancy introduced into information data has a superior performance over nonbinary LDPC (NB-LDPC) codes with both linear-time encoding and decoding.