Research On Serially-Concatenated Low Density Generator Matrix

With the development of wireless communications, the demand of system reliability and effectiveness increases. Turbo and LDPC codes obtained good performance near the Shannon limit, but the complexity of the two codes are not very low, so there is still some space to do some optimization for the implementation.This paper presents a low-density generator matrix (LDGM) code, which uses iterative decoding method, so the decoding complexity is low. And also because it is a system code, the complexity of the encoding process is also low, which can be realized easily. However, because one identity matrix exists in the system check matrix, there are some variable nodes whose degree is 1, resulting that the message of some nodes can not be updated, so there is an error floor in the separate LDGM platform. In order to overcome the error floor, serially concatenated codes is introduced. Serially concatenated code consists of inner code and outer code. The output message of the inner decoder is not completely corrected, when it comes to the outer decoder, the error message is much less to the outer one compared to the instant message. So the outer decoder can correct the error easily, and the whole performance is better. Because the spectrum resources are limited, BICM-ID is an effective way to improve the wireless channel transmission efficiency, with the combination of the channel coding and modulation technique. Besides, because of the information feedback iteration between the demodulator and decoder, the performance is improved.This paper focuses on the LDGM codes, specifically using the formula to describe the messages iterative decoding process. Analyze the complexity and performance, getting the conclusion that decoding and encoding complexity of LDGM code are very low, but the performance of is not good. Find out the impact factors of the performance by quantitative analysis. Simulation results show the performance different parameters. Introduce the concept of a serially concatenated code to eliminate error platform, describe encoding and the message iteration of decoding process in detail, and compare two different message passing methods from both complexity and performance aspects, getting the result that serially concatenated LDGM code can ensure the low complexity and can also achieve good performance results. This paper also applies the SCLDGM code in BICM-ID system, effectively improving the transmission efficiency of the wireless channel. And the performance of method with feedback iteration between demodulator and decoder is better, and this conclusion is verified by simulation.