A novel construction of irregular LDPC codes is presented. The proposed construction allows one to obtain a number of codes with different length from a single prototype code with a parity check matrix given by H=[Hz Hi], where Hz specifies the well-known zigzag pattern in the corresponding Tanner graph. The parity check matrices for longer codes are obtained as [Hz' Pi diag(Hi,...,Hi)], where Hz' specifies a longer zigzag pattern depending on the number of matrices Hi used, and Pi represents some permutation. This allows one to construct the decoder for a longer code by reusing hardware components developed for decoding the prototype code.