Bitwise Log-Likelihood Ratios for Quadrature Amplitude Modulations

For an increase in spectral efficiency and improvement of error performance, a high-order modulation and an advanced channel coding scheme are jointly used for many digital communication systems. In this paper, a new and simple method for calculating bitwise log-likelihood ratios which are required for soft decision decoding is proposed for M-ary quadrature amplitude modulations. The mean square error of the proposed scheme is fairly improved when compared with the well-known Min approximation. In addition, the decoding error probability that is evaluated using a turbo code is in agreement with the performance obtained by the exact bitwise log-likelihood ratios that accompany high computational complexity.