Low-Complexity LLR Calculation for Gray-Coded PAM Modulation

Higher-order modulation schemes are employed to improve the spectral efficiency in modern communication systems. However, the conventional Max-Log-MAP symbol-to-bit demapper suffers from a large computational burden. To cope with this problem, this letter proposes a novel log-likelihood ratio computation algorithm for Gray-coded higher-order pulse-amplitude modulation (PAM). The proposed method reduces the order of complexity from O(2
^M
) to O(M) without any difference of the LLR values compared with the Max-Log-MAP demapper, where M is the number of bits in one PAM symbol. Moreover, it is also shown that the proposed algorithm achieves superior complexity reduction compared with a recently proposed low-complexity demapper.