In this paper we present a class of structured LDPC codes over GF(q) which are suitable for efficient encoding. We derive the conditions under which the Phi matrix defined by Richardson & Urbanke in (2001) is an identity matrix over GF(q). If the parity-check matrix satisfies the derived conditions, the inversion of the Phi matrix can be removed in encoding process so that the computational complexity grows linearly with the code length. Simulation results show that efficiently encodable structured LDPC codes have no performance degradation due to the constraint on their design structure, compared with randomly constructed LDPC codes.

In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.