Abstract: Optimization of binary LDPC (Low-Density Parity-Check) codes for application to binary PSK modulation has been demonstrated in the literature, on the basis of Monte-Carlo method proposed by Davey(1998). The lack of rotational symmetry in a generic q-ary signal constellation, however, limits the application of Daveys method. This paper proposes an efficient Davey-type Monte Carlo technique for code optimization within the category of quasi-regular codes, so that one can directly combine the optimized LDPC code over GF(q) with arbitrary q-ary modulation to achieve bandwidth efficiency in transmission. The validity of the proposed design procedure is illustrated through examples combining quasi-regular LDPC codes with MQAM and MPSK signaling schemes.