Recursive Approximation of Bitwise LLRs for Gray-Coded Generalized PAM and QAM

It is known that coded system performance can be improved by simply generalizing the square-shaped quadrature amplitude modulation (QAM) constellation to a rectangular-shaped QAM. In the present letter a new method of approximating bitwise log-likelihood ratios is proposed and analyzed for efficient decoding in the system employing generalized QAMs. According to numerical results in additive white Gaussian noise (AWGN) channel, the proposed scheme provides a performance comparable to the Min-approximation especially at high $E_{s}/N_{0}$ , while achieving reduction in computational complexity.