Design And Optimization Of Coded Modulations Based On Sparse Factor Graphs

Factor graph is a useful tool to analyze and design iterative reicever, while coded modulation is an efficient scheme to approach the Shannon channel capacity at high spectral efficiency. This dissertation investigates three coded modulation schemes based on sparse factor graphs. The main topics are shown as follows.1. It proposes an LDPC coded modulation scheme based on superposition coding.(1) It designs and optimizes the modulated signal constellation on the criterion that the mutual information of channel input signals and output signals is maximized.(2) It also proposes a demapping algorithm with low complexity based on the node-by-node message passing strategy. Meanwhile it analyzes the probability density function of demapping output.(3) It proposes a method to optimize the degree distribution of LDPC code used in this coded modulation scheme. The main innovation is to optimize the degree of LDPC codes used coded modulation scheme by jointly considering coding and modulation. Compared with the conventional LDPC coded modulation, this scheme has a better performance.2. It designs and optimizes the low-density lattice codes (LDLC) used for AWGN channels and ISI channels.(1) It proposes the low-complxity decoding algorithm based on single Gaussion approximation in which the passing messages are represented by single Gaussian distribution instead of Gaussion mixture. With the assumption of single Gaussian approximation and all-zero lattice point transmission, it proposes the design and optimization scheme for LDLC codes. Simulations are employed.(2) It researches the LDLC code design for ISI channels. It proves that introducing the ISI into the primary LDLC codes can achieve the extra nominal coding gain, which can be utilized by shaping operation. Similary the LDLC codes for ISI channels are designed to match the specified channel condition. The optimized LDLC codes for ISI channel can achieve the capacity of ISI channels. The main innovations are to optimize the parity check matrix of LDLC codes for AWGN channel and ISI channels. Since the channel conditions are matched naturally when desiging, the optimized LDLC codes for AWGN channel outperform the non-binary LDPC codes. Also compared with the LDPC codes designed for ISI channels, the optimized LDLC codes have a better performance.3. It proposes three aspects of the generalized low-density generator matrix codes (G-LDGM codes), including the low-complexity parametric Gassian belief propagation (BP) decoding algorithm and the convergence analysis of decoding algorithm, the signal design as well as its shaping methods.(1) It proposes the parametric Gaussian BP decoding algorithm based on the sparse generator matrix. The convergence analysis is employed and proved.(2) It designs the G-LDGM codes for AWGN channels with and without power restrictions. The G-LDGM codes via spatial coupling are designed.(3) It designs a shaping method for the G-LDGM codes used for AWGN channel with power restrictions. The main innovation is to optimize the sparse generator matrix of G-LDGM codes. Compared with the LDLC codes, the optimized G-LDGM codes have a better BP threshold and lower encoding complexity.