Research On Low-Density Parity-Check Codes And Iterative Decoding Systems

Low-Density Parity-Check (LDPC) codes have been demonstrated to be a kind of capacity approaching error-correcting code, and are finding their promising applications in many fields. The turbo principle in sum-product algorithm is widely used to design the receiver to improve system performance. In this paper, the decoding algorithm and performance of LDPC codes is discussed for some important channels, and some important issues for bit-interleaved coded modulation with iterative decoding(BICM-ID), such as constellation mapping, channel estimation, are studied. The main contents can be summarized as follows:1. Following the idea of shuffled BP decoding algorithm, an improved version of shuffuled BP algorithm is proposed. Simulaiton shows that the improved shuffled BP algorithm can speed up the convergence of decoding. Based on the equivalent of check node and variable node of bipartite graph, a check-node based shuffled algorithm is proposed. In addition, it is easy to see that our improved version of shuffled BP algorithm can be applied to the check-node based shuffled BP algorithm and other types of shuffled BP algorithm, such as group shuffled BP algorithm, replica shuffled algorithm, etc.2. Sum-product decoding algorithm is discussed for additive impulse noise channels. When sum-product algorithm is used for additive impulse noise channel, the initial channel log-likely ratio (LLR) messages have no close expression, and moreover, computation of the initial channel LLR is very difficult. By reexamined the computation of the initial channel LLR messages for AWGN channels, Least Square (LS) metric is proposed to compute the initial LLR messages for additive impulse noise channel, and the decoding algorithm is simplified. Since the characteristics of impulse noise, sum-product algorithm with LS metric occurs error floor. In order to dissolve this problem, another robust metric, i.e., Huber metric is introduced to compute the initial LLR messages. The performance of sum-product algorithm based Huber metric is analyzed by EXIT chart. Simulation results show that sum-product algorithm based Huber metric can achieve good performance.3. Decoding algorithm and performance of LDPC is studied for Nakagami-fading channels. Two important conditions, symmetry condition and stability condition, is discussed for AWGN, Rayleigh, Rice and Nakagami channels respectively. It is proved that the PDF of the initial channel LLR message in sum product algorithm satisfies the symmetry condition and the stability is given when the channel is Nakagami fading channel. And here, we re-derive the stability of sum product for Rice channel. Also, we discussed the sum product decoding and performance of LDPC when the Nakagami parameter is multiples of 1/2 and channel state information (CSI) is partially known. Simulation result shows that, with the increase of Nakagami parameter, the performance of sum product with partial CSI is close to that of sum product with perfect CSI.4. Signal mapping is studied for BICM-ID systems. In LDPC-based BICM-ID systems, EXIT chart is proposed to analyze constellation design. Six kinds of signal mapping is analyzed using EXIT chart, and simulation results verify the validity of EXIT chart for constellation...