Research On Decoding Algorithms For Non-binary LDPC Codes

Low-Density Parity-Check Code was first discovered by Gallager in the early 1960s and was considered as another class of Shannon-Limit approaching codes besides Turbo codes. Compared with Turbo codes, LDPC codes are predominant for their low decoding complexity and flexible coding speed. Especially, non-binary LDPC codes are more capable of rectifying burst and random noises, are suitable for high-order modulation system. Non-binary LDPC codes are the hot issue in the communication field.For the moment, there have been sophisticated researches about binary LDPC codes. However, for non-binary LDPC codes, their high decoding complexity limits their applications, although many conclusions about binary LDPC codes could be used. Thus, how to reduce the decoding complexity as the performance is nearly not changed has become the choke point in the research of binary LDPC codes. This paper investigates the decoding algorithms and brings forward a new algorithm with low computation complexities. The main investigative work included is shown as follows.1. Based on the coding and decoding theory of binary LDPC codes, this paper analyses the aim of studying non-binary LDPC codes and shows the reasons for the difference between non-binary and binary.2. Based on the theory of non-binary LDPC codes, this paper investigates the existing traditional and simple decoding algorithms, such as Belief Propagation algorithm, Log Likelihood Ratio-Belief Propagation algorithm, Fast Fourier Transform-Belief Propagation algorithm, Extended Min Sum algorithm and so on, with lots of simulations to prove the performances.3. This paper proves the equipollence between Fast Fourier Transform and Fast Hadamard Transform in the decoding process of non-binary LDPC codes according to the simulations.4. Based on Log Likelihood Ratio-Fast Hadamard Transform-Belief Propagation algorithm which has been introduced to the logarithm field and the"truncating tail"thought in EMS algorithm, this paper brings forward a new decoding algorithm with low decoding complexity, small storage and short used time. Moreover, it studies and analyses the shortages in the new algorithm and brings forward some improved ideas to make them up, and finally validates the predominance of the new algorithm and the effect of the improved ideas.