What is Girth

This chapter presents performance of a new technique for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) encrypted codes based on a row division method. The new QC-LDPC encrypted codes are flexible in terms of large girth, multiple code rates, and large block lengths. In the proposed algorithm, the restructuring of the interconnections is developed by splitting the rows into subrows. This row division reduces the load on the processing node and ultimately reduces the hardware complexity. In this method of encrypted code construction, rows are used to form a distance graph. They are then transformed to a parity-check matrix in order to acquire the desired girth. In this work, matrices are divided into small sub-matrices, which result in improved decoding performance and reduce waiting time of the messages to be updated. Matrix sub-division increases the number of sub-matrices to be managed and memory requirement. Moreover, Prototype architecture of the LDPC codes has been implemented by writing Hardware Description Language (VHDL) code and targeted to a Xilinx Spartan-3E XC3S500E FPGA chip.