Study On Some Key Problems Of Low-Density Parity-Check Codes

Low-Density Parity-Check (LDPC) Codes are a class of capacity approaching error-correcting codes. With long code-lengths, LDPC codes can even outperform Turbo codes. Due to the advantages of LDPC codes, such as lower complexity of decoding and lower error floor, their applications in reliable communications have received great interests and have become one of most attractive field in channel coding community.This thesis investigates some key problems of Low-Density Parity-Check (LDPC) codes with theoretical analysis and simulation. The main results and contents are as follows.First, we generally introduced the method of constructing LDPC Codes, and then gave the method of constructing Quasi-cyclic LDPC Codes, and an approach to construct efficiently encodable LDPC Codes is presented at last. The encoder of the proposed LDPC code may be characterized by a group of interleavers and convolutional encoders linked in parallel. And the corresponding parity check matrix can be decomposed into two sub-matrices which are determined by the interleavers and the generator matrices of convolutional encoders, respectively. Every interleaver is designed based on the equivalent representations of a finite filed element, so named a finite filed interleaver. With this structure, extraordinary fast encoding of LDPC codes can be achieved. By optimizing the two sub-matrices respectively, an overall efficiently encodable LDPC code with good decoding performance is obtained.The principles of hard-decision decoding and soft-decision decoding are systematically summarized. In the hard-decision decoding hand, Bit-flipping (BF) algorithm for hard-decision decoding is discussed, and the LDPC Codes with higher rate are more appropriate for the use of BF algorithm is concluded; In the soft-decision decoding hand, firstly, we introduced and compared the soft-decision decoding algorithm of the three measures, the equations for updating messages in sum-product algorithm are derived and the most excellently performance of the LLR measure is analyzed. Secondly, between simulation performance and the operation complexity we compromise that Normalized MSA algorithm is optimality in STIMI standards.By theoretical analysis and simulation, quantization decoding of LDPC codes is studied. We analyze the superiority performance of the LLR measure quantization decoding, and design the ultimate LDPC Codes quantization decoding scheme of STIMI standards.In the end, Simulations are performed for the purpose of exploiting the applications of LDPC codes in fading channels and two conclusions are abtained. The first is that LDPC Codes with lower rate have a stronger anti-multipath fading capabilities. The second is that the inherent interleaving effects following the very sparse structure are investigated, which enable the tolerance of LDPC codes for some faster fades or longer bursts.