Dual Square-Shaped Constellation With Two-Layer Coding and Successive Demapping for Odd-Bit QAM

Odd-bit quadrature amplitude modulations (QAMs) can achieve higher data rates than even-bit QAMs in some signal-to-noise (SNR) regions but they have not been used in wireless communication standards due to its high demapping complexity. In this paper, we propose a novel constellation for odd-bit QAM, called dual square-QAM (DSQAM). It consists of two regular even-bit square-QAMs spaced apart by a shift value in the diagonal direction. We also propose a two-layer coding which effectively exploits the structural property of the constellation and a successive demapping to use the decoding result of the first layer for the second layer. The proposed DSQAM is enhanced by the two-layer coding and successive demapping, which consists of multi-level coding and bit-interleaved coded modulation (BICM). The asymptotic information rate (AIR) under the coding scheme is maximized for a given channel state by adjusting the shift value. The AIR analysis shows that the DSQAM with the two-layer coding and the successive demapping is the best among conventional QAMs with the BICM for a wide range of SNR values. Based on the structure of the constellation, we propose a low-complexity implementation of the max-log approximation to calculate the log-likelihood ratio for practical use. It is shown via simulations over the additive white Gaussian channel that the proposed DSQAMs with the coding scheme have significant block error rate gains over the conventional odd-bit non-square-QAM (NSQAM) and cross-QAM (XQAM) with bit-interleaved coded modulation. The computational complexity for demapping is reduced by up to 10% and 59% compared to NSQAM and XQAM, respectively.