Efficient Construction for QC-LDPC Convolutional Codes with Periodic Bit-Filling

QC-LDPC-C (Quasi-Cyclic Low Density Parity-Check Convolutional) codes are with low encoding and decoding complexity and can achieve decoding performance approaching the Shannon limit. However, the construction of the parity check matrices need to be free of the length-4 cycles, and the computational complexity of direct construction will increase exponentially without considering the characteristics of the matrices. The construction for QC-LDPC-C codes with periodic bit-filling method is proposed. With the periodicity of the base check matrix, the proposed method firstly fills the deterministic submatrices to realize fast encoding; then it avoids all possible length-4 cycles by periodic filling in the construction of random submatrices. Thus the base check matrix without cycles of length-4 can be obtained, and the girth of expanded check matrix is at least 6. LDPC-C codes with different parameters are used to compare with the constructed QC-LDPC codes. Experimental results show that the codes constructed with proposed method can achieve better performance and lower encoding and decoding complexity.