Algorithms and Implementation of Long Euclidean-Geometry LDPC Codes for Space Communications

The encoding technique of long Euclidean-geometry LDPC codes is studied to meet the need of space missions. Firstly, the encoding algorithm is analyzed. The parity-check matrix is constructed by the incidence vector of points and lines in Euclidean geometry. The method for computing generator matrix is derived from solving matrix equation over GF(2). Secondly, according to the characteristics of quasi-cyclic matrix, a new encoding circuit of using feedback shift registers is proposed. Last, serial encoding circuit for resource-optimization and parallel encoding circuit for speed-optimization are designed respectively and implemented on Xilinx XC4V SX55 FPGA, with both reaching high encoding speed. The results show that the encoding scheme in this paper performs efficiently enough for space communications.