| Low-Density Parity-Check (LDPC) channel coding scheme is widely studied for its near Shannon capacity performance just like the Turbo codes. The LDPC codes have several advantages over the Turbo codes and even more promising for future applications. As a result, the LDPC codes are one of the hottest topic in today's coding theory research.The LDPC codes can be roughly divided into two categories, the randomly constructed and the systematically constructed. These two type of codes both have their own advantages and drawbacks: systematically constructed LDPC codes have simple coding structure and the encoding complexity is therefore very low, while the randomly constructed LDPC codes although have a higher encoding complexity, but they have no constraints on the code block-length and the code rate which is essential in today's communication applications with very strict constraints on the code rate and the code block-length defined by the standards. In this paper, we summarize the efforts made so far in the LDPC coding theory research, on the basis of which we propose a new optimization procedure for the randomly constructed LDPC codes. Simulation results show that after optimization the randomly designed LDPC codes have a significant performance improvement. Also, simulations show that under low code rates, the randomly designed LDPC codes have an even better performance than the systematically constructed LDPC codes in the same decoding environment.On the other hand, the binary LDPC codes cannot be used directly in high order channels. The recent research on higher order LDCP codes made it possible for application in high order modulated channels. In the paper, we will study and analysis the high order LDPC codes and finally prove that: although with a relatively high decoding complexity, the high order LDPC codes combined with the high order modulation render a better performance than other coded modulations schemes that uses binary LDPC codes under high order modulated channels. |
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