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

Analysis and design of three-stage concatenated color-shift keying

Visible Light Communication (VLC) relies on abundant unlicensed bandwidth resources. As an attractive high-data-rate modulation scheme designed for VLC, Color Shift Keying (CSK) assisted modulation is analysed. We commence our study from an uncoded M-CSK scheme relying on the joint Maximum Likelihood (ML) Hard-Detection (HD) of three colors, when communicating over an AWGN channel, where both empirical and analytical results are provided. We invoke EXtrinsic Information Transfer (EXIT) charts for designing a Maximum A-posteriori Probability (MAP) based Soft-Detection (SD) aided iterative receiver jointly detecting the three colors. Based on the EXIT characteristics of M-CSK, we design different signal labeling strategies for diverse color constellations and detection schemes, which are capable of achieving a substantially improved Bit Error Ratio (BER) performance. Thus, given a fixed transmission power, a CSK system using our proposed signal labeling is capable of increasing the reliable data transmission distance by about 30%

Constellation Design for Channels Affected by Phase Noise

In this paper we optimize constellation sets to be used for channels affected by phase noise. The main objective is to maximize the achievable mutual information of the constellation under a given power constraint. The mutual information and pragmatic mutual information of a given constellation is calculated approximately assuming that both the channel and phase noise are white. Then a simulated annealing algorithm is used to jointly optimize the constellation and the binary labeling. The performance of optimized constellations is compared with conventional constellations showing considerable gains in all system scenarios.Comment: 5 pages, 6 figures, submitted to IEEE Int. Conf. on Communications (ICC) 201

Signal Shaping for BICM at Low SNR

The mutual information of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR), i.e., in the wideband regime. A new linear transform that depends on bits' probabilities is introduced. This transform is used to prove the asymptotical equivalence between certain BICM systems with uniform and nonuniform input distributions. Using known results for BICM systems with a uniform input distribution, we completely characterize the combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit -1.59 dB. The main conclusion is that a BICM system achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube, which is the same condition as for uniform input distributions. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR mutual information of BICM systems, in addition to what is provided by geometrical shaping. These analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping of BICM can improve the mutual information in the low and medium SNR range over any coded modulation system with a uniform input distribution