Abstract: The construction of parity check matrices for QC-LDPC-C (Quasi-Cyclic Low Density Parity-Check
Convolutional) codes needs to be free of length-4 cycles，and the computational complexity of direct
construction will increase exponentially without considering the characteristics of matrices． The construction for
QC-LDPC-C codes based on periodic filling with offsets of sub-matrices is proposed． With the periodicity of the
base check matrix，the proposed method fills the deterministic sub-matrices to realize fast encoding; during the
construction for random sub-matrices，the optimized selection with offsets of sub-matrices is utilized to ensure
that the obtained matrix after each selection for sub-matrix position and periodic expansion satisfies the
expended structure without length-4 cycles． The base check matrix whose expanded matrix is free of length-4
cycles 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-C codes． Experimental results show that the
codes constructed with proposed method can achieve better performance and lower encoding and decoding
complexity．

Key words: quasi-cyclic low density parity-check convolutional ( QC-LDPC-C) code, code construction,
periodic filling, girth, fast encoding