A Class of Structured LDPC Codes Over GF(q) for Efficient Encoding

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.