Polar Decomposition of Mutual Information over Complex-Valued Channels

A polar decomposition of mutual information between a complex-valued channel's input and output is proposed for a input whose amplitude and phase are independent of each other. The mutual information is symmetrically decomposed into three terms: an amplitude term, a phase term, and a cross term, whereby the cross term is negligible at high signal-to-noise ratio. Theoretical bounds of the amplitude and phase terms are derived for additive white Gaussian noise channels with Gaussian inputs. This decomposition is then applied to the recently proposed amplitude phase shift keying with product constellation (product-APSK) inputs. It shows from an information theoretical perspective that coded modulation schemes using product-APSK are able to outperform those using conventional quadrature amplitude modulation (QAM), meanwhile maintain a low complexity

High-Rate Regular APSK Constellations

The majority of modern communication systems adopts quadrature amplitude modulation (QAM) constellations as transmission schemes. Due to their square structure, however, QAM do not provide satisfying protection to phase noise effects as the number of constellation points grows, increasing at the same time their peak to average power ratio (PAPR). This requires an expensive power amplifier and oscillator at the transmitter to guarantee low distortion, complicating the adoption of dense transmission schemes in practical high-data rate systems. In this paper, we construct a coded modulation scheme based on regular amplitude and phase shift keying (RAPSK) modulations. We propose a novel multilevel coding (MLC) labeling for the constellation points separating amplitude and phase domains. We provide a novel multistage decoding (MSD) scheme allowing for a low-complexity log-likelihood ratio (LLR) calculation for soft-input decoding of component codes, along with a suitable rate design. Finally, we compare the proposed scheme with state-of-the-art QAM constellations and optimized constellations in the presence of phase noise