Design of QC-LDPC Code with Continuously Variable Length

Based on the theory of finite polynomial ring, a novel code design method for Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes with continuously variable length is proposed. When the cardinal number of the ring is larger than a certain threshold, the shift offset values can be formulated by the parameters selected in the ring. Thus all H matrices constructed by them have larger girth. In the design, the cardinal number of the ring is a continuously variable integer, which has a linear relation with the code length, so that the code length can be increased continuously. Analyses and proofs show that, the method can enlarge the number of QC-LDPC codes greatly, which can serve the adaptive link systems better.