Iterative Decoding

In this paper, we concluded and induced all kinds of iterative decoding algorithms used in Turbo and LDPC codes. We programmed and simulated these decoding algorithms, and gave the simulated results. Based on the simulantion results, the near-shannon-limit characteristic of the two famous codes has been presented clearly. What we focus on is the M-ary modulated LDPC codes. Firstly, the M-ary modulated Min-Sum algorithm which based on Maximum Liklihood (ML) is provided, however, can not be applied to actual decoding due to its complexity. By applying the so called Generalized Distributive Law (GDL), we simplified the Min-Sum decoding for M-ary modulated LDPC codes based on Maximum Likelihood, and obtained what we called Enhanced Min-Sum algorithm. Also through analyzing the slight differences between Min-Sum algorithm and Belief Propagation algorithm, we provided a new algorithm for M-ary modulated LDPC codes, which we call Enhanced BP algorithm. Simulation results show that the enhanced algorithms have improved the decoding results comparing with the corresponding algorithms which just based on calculating the receiving log-likelihood ratio in the initialization step and then applying directly the algorithms used for binary case. For the Enhanced Min-Sum algorithm, the BER performance outperforms the corresponding bit-based algorithm for an order under the same signal-to-noise ratio. For Enhanced BP algorithm, the results are better with a 0.2dB improvment at a BER rate of 10^-5. The theoretical analysis shows that the enhanced algorithms are not so complicated and simulation results indicate that the actual number of iteration is less which further reduces the decoding complexity. Based on simulation, we have done some further research on the enhanced algorithms including unequal error protection and iterative decoding convergence. Although it is well known that to make a good theoretical analysis for iterative decoding is very difficult, yet we have tried to do so via using two famous powerful tools, i.e. the Density Evolution functions and the Extrinsic Information Transfer Chart (EXIT).