Shaping gain of LDPC Coded-QAM transmitting systems with non-uniform constellation

In this paper shaping gains of regular (3,6) LDPC Coded-QAM transmitting systems with nonuniform QAM constellation are presented over AWGN channel. The influences of code rate, frame length, the order of non-uniform QAM constellation, and the finite fields GF(q) of LDPC codes on shaping gain are investigated. It is found that shaping gain of proposed system with non-uniform 64QAM constellation for binary LDPC codes (R=1/2) can be obviously achieved by middle frame length, and can be improved further with the increase of frame length. Meanwhile it is found that under non-uniform 16QAM constellation for binary LDPC code(R=1/2) there is no shaping gain improvement with the increase of frame length, but the shaping gains of nonuniform 16QAM and 64QAM both are increased, even the former is no less than the latter when we change the finite fields GF(q) of LDPC codes from 2 to 16. The shaping gain can disappear as the binary code rate increases to 3/4 in proposed system.