欧氏几何LDPC长码的卫星通信编码方案研究

Research on Long Euclidean Geometry—Based LDPC Coding Scheme for Satellite Communications

研究了基于欧氏几何的LDPC码的编码原理与技术,基于航天任务提出并实现了高效可行的卫星通信编码方案;基于欧氏几何讨论了编码算法,利用欧氏空间中子空间的关联向量构造校验矩阵,构造伽罗瓦域上的矩阵方程求解生成矩阵;结合准循环生成矩阵的结构特点,建立了一种新的基于移位寄存累加结构的编码电路,并基于该电路提出完整的编码设计方案;利用XC4V SX55 FPGA,分别实现了串并行编码电路并采用标准置信度传播译码算法验证了编码算法的正确性。

Euclidean--geometry LDPC encoding theory and technique is researched in this paper. An efficient and feasible satellite com- munication encoding scheme is proposed and implemented based on space missions. The encoding algorithm based on Euclidean--geometry is discussed. The parity-- check matrix is constructed by the incidence vector of Euclidean subspace and the generator matrix is derived from sol ring the matrix equation over Galois field. According to the quasi--cyclic feature of generator matrix, a new encoding circuit of shift--regis- ter- adder--accumulator is proposed and a complete encoding scheme is proposed based on this circuit. Serial and parallel encoding circuit are designed respectively and implemented on XC4V SX55 FPGA and the correctness of encoding algorithm is verified by standard belief propaga- tion decoding algorithm.