The Realization Algorithm And Performance Analysis Of LDPC Code

LDPC (Low Density Parity Check) code is a kind of linear block code that defined by very sparse parity matrix or tanner graph, and it is also called Gallager code since Gallager initially presented it. LDPC code were rediscovered and shown to form a class of Shannon-limit-approaching codes in the late 1990s. These codes, decoded with iterative decoding based on belief propagation, such as the sum-product algorithm, achieve amazingly good error performance. Ever since their rediscovery, design, construction, decoding, efficient encoding, performance analysis, and applications of these codes in digital communication and storage systems have become the focal points of research.LDPC code belongs to the linear block code which is encoded by the information sequence multiplies generator matrix. Although the parity-check matrix of LDPC code is sparse, the generator matrix is not. The encoding complexity of it is linearly proportional to the square of code length. The code . length is very large when it be used. Also, a significant amount of memory is needed to store their parity-check matrices. In this way, the encoding problem of LDPC codes may be an obstacle for their applications because they have high encoding complexity. This paper mainly studies encoding problem of LDPC codes.Firstly, the paper introduces the fundamental principle of LDPC code, including LDPC code's basic conception, construction, encoding and decoding algorithm. Then discusses conventional encoding algorithm and efficient encoding algorithm, and expatiates the principle of Message Passing and SPA which has the best performance in decoding algorithm. Secondly, this paper introduces a kind of optimized code algorithm , first uses the Efficient code algorithm which proposed by Richardson and Urbanke optimizes the LDPC code check matrix , then mainly studies on the 4- circle in its bipartite graph, proposes a kind of algorithm cancels the 4- circle in the check matrix, realizes its program design in amalgamation program fashion of Matlab. It avoids the repeated iteration in the decoding process of LDPC codes and noticeably improves the bit error ratio capability of short frame LDPC codes. Moreover, it analyzes different parameters for the performance of LDPC codes and draws some conclusions. Last, this paper realizes the whole LDPC encoder using VHDL language based on CPLD.