Maximum Euclidean distance network coded modulation for asymmetric decode-and-forward two-way relaying

Network coding (NC) compresses two traffic flows with the aid of low-complexity algebraic operations, hence holds the potential of significantly improving both the efficiency of wireless two-way relaying, where each receiver is collocated with a transmitter and hence has prior knowledge of the message intended for the distant receiver. In this contribution, network coded modulation (NCM) is proposed for jointly performing NC and modulation. As in classic coded modulation, the Euclidean distance between the symbols is maximised, hence the symbol error probability is minimised. Specifically, the authors first propose set-partitioning-based NCM as an universal concept which can be combined with arbitrary constellations. Then the authors conceive practical phase-shift keying/quadrature amplitude modulation (PSK/QAM) NCM schemes, referred to as network coded PSK/QAM, based on modulo addition of the normalised phase/amplitude. To achieve a spatial diversity gain at a low complexity, a NC oriented maximum ratio combining scheme is proposed for combining the network coded signal and the original signal of the source. An adaptive NCM is also proposed to maximise the throughput while guaranteeing a target bit error probability (BEP). Both theoretical performance analysis and simulations demonstrate that the proposed NCM can achieve at least 3 dB signal-to-noise ratio gain and two times diversity gain

Network coded modulation for two-way relaying

Network coding compresses multiple traffic flows with the aid low-complexity algebraic operations, hence holds the potential of significantly improving both the power and bandwidth efficiency of wireless networks. In this contribution, the novel concept of Network Coded Modulation (NCM) is proposed for jointly performing network coding and modulation in bi-directional/duplex relaying. Each receiver is colocated with a transmitter and hence has prior knowledge of the message intended for the distant receiver. As in classic coded modulation, the Euclidian distance between the symbols is maximized, hence the Symbol Error Ratio (SER) is minimized. Specifically, we conceive NCM methods for PSK, PAM and QAM based on modulo addition of the normalized phase or amplitude. Furthermore, we propose low complexity decoding algorithms based on the corresponding conditional minimum distance criteria. Our performance analysis and simulations demonstrate that NCM relying on PSK is capable of achieving a SER at both receivers of the NCM scheme as if the relay transmitted exclusively to a single receiver only. By contrast, when our NCM concept is combined with PAM/QAM, an SNR loss (<1.25dB) is imposed at one of the receivers, usually at the one having a lower data rate in a realistic different rate scenario. Finally, we will demonstrate that the proposed NCM is compatible with existing physical layer designs

Design of APSK Constellations for Coherent Optical Channels with Nonlinear Phase Noise

We study the design of amplitude phase-shift keying (APSK) constellations for a coherent fiber-optical communication system where nonlinear phase noise (NLPN) is the main system impairment. APSK constellations can be regarded as a union of phase-shift keying (PSK) signal sets with different amplitude levels. A practical two-stage (TS) detection scheme is analyzed, which performs close to optimal detection for high enough input power. We optimize APSK constellations with 4, 8, and 16 points in terms of symbol error probability (SEP) under TS detection for several combinations of input power and fiber length. Our results show that APSK is a promising modulation format in order to cope with NLPN. As an example, for 16 points, performance gains of 3.2 dB can be achieved at a SEP of 10^-2 compared to 16-QAM by choosing an optimized APSK constellation. We also demonstrate that in the presence of severe nonlinear distortions, it may become beneficial to sacrifice a constellation point or an entire constellation ring to reduce the average SEP. Finally, we discuss the problem of selecting a good binary labeling for the found constellations. For the class of rectangular APSK a labeling design method is proposed, resulting in near-optimal bit error probability.Comment: Submitted to IEEE Transactions on Communication