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

Shaping gains of regular (3,6) LDPC Coded-QAM transmitting systems with non-uniform 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 non-uniform 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.