The circulate property of generator matrices of protograph LDPC codes

The LDPC application involves the problem: encoding complexity. Since the generator matrices are dense and with random positions of "1s", the encoder needs to store every "1" of the generator matrices by using huge chip area. To solve problem, we need to design the LDPC codes with block cyclic generator matrices. This paper reveals that the protograph LDPC codes can have lower encoding complexity under the condition of the proposed theorem that the parity check matrices of the LDPC codes are nonsingular and circulate. The circulate property of generator matrix of protograph LDPC codes can be obtained from the quasi-cyclic parity check matrix of protograph LDPC codes. Thus it can reduce the encoding complexity. We give an algorithm of protograph LDPC codes with fast encoding based on the theorem, and it verifies that protograph LDPC codes with circulate property of generator matrices can simplify encoder hardware implementation.