A Compact Construction for Nonbinary LDPC Codes Using Permutation Polynomials

A compact construction for nonbinary low-density parity-check (LDPC) codes over GF(q) (q>2) using permutation polynomials (PPs) is proposed in this paper. Following the previous compact construction for binary LDPC codes using quadratic permutation polynomials (QPPs) over integer rings, a QPP whose coefficients are chosen for maximizing the girth is used for determining all the positions of nonzero elements in the parity check matrix of a regular nonbinary LDPC code. Moreover, it is proposed to use a linear permutation polynomial (LPP) over GF(q) for determining the distribution of nonzero elements of GF(q) at the nonzero positions. Computer simulation results of LDPC codes over GF(8) have shown that the propose compact construction can attain similar error correction performance with Mackay's random construction for nonbinary LDPC codes.