Covariance-Aware Demapping on Fourier-Curve Constellations

Injecting artificial noise (AN) along the tangent space of a curved constellation makes each transmitted symbol induce a Gaussian observation with a symbol-dependent rank-one covariance, so the matched maximum-likelihood (ML) decoder differs from the Euclidean nearest-neighbor decoder by a single rank-one correction per candidate. We develop a baseband-demapper realization of this correction for the Fourier-curve constellation and instantiate a regular $(3,6)$ low-density parity-check (LDPC)-coded link at $(k,M){=}(20,64)$. Against four baselines (Euclidean-mismatched, flat-constellation isotropic-AN, no-AN, and same-spectral-efficiency narrowband), the matched decoder extends the BLER${=}10^{-1}$ operating range by approximately $5$\,dB over the Euclidean-mismatched counterpart on the same tangent-AN transmitter, at a cost of $2kM$ additional multiply-accumulate operations per symbol ($+50\%/+100\%$ under residual/template-correlation accounting) and a $20$\,KB constellation--tangent lookup table ($10$\,KB incremental over a Euclidean template-only LUT). A bit-interleaved coded-modulation achievable-rate (BICM-AIR) computation supports the same matched-metric advantage at the tested labeling and max-log demapper, indicating that the BLER gain is not merely an artifact of this particular LDPC simulation, and a Woodbury extension generalizes the rank-one correction to per-tone Ricean fading. In the tested Monte-Carlo runs, a design-aware bounded-search eavesdropper without the phase-key shows no successful LDPC decoding at any tested $k\in\{2,8,20\}$ within a $B{=}10^{3}$ non-code-aided search budget; code-aided, multi-frame, and known-preamble attacks are left to follow-up work. LUT quantization down to $6$ bits yields no measurable coded-BLER degradation at the tested operating points.

Matched and Euclidean-Mismatched Decoding on Fourier-Curve Constellations with Tangent Noise

We study matched and Euclidean-mismatched decoding on finite Fourier-curve constellations with tangent-space artificial noise. Each hypothesis induces a Gaussian law with symbol-dependent rank-one covariance. We derive exact Euclidean pairwise errors for arbitrary pairs and an exact Gaussian-expectation representation for matched decoding on bilaterally tangent-orthogonal pairs. For uniform even constellations, the Euclidean side yields explicit distance spectra and symbol-error bounds across all offset classes; the matched side is exact on antipodal pairs and benchmarked numerically at the full-codebook level via Monte Carlo. By isolating the detection-theoretic consequence of tangent-space artificial noise, these results clarify analytically how noise fraction and constellation density enter the mismatch behavior; secrecy-rate implications require additional channel and adversary modeling.

ChatGPT-Like Large-Scale Foundation Models for Prognostics and Health Management: A Survey and Roadmaps

Prognostics and health management (PHM) technology plays a critical role in industrial production and equipment maintenance by identifying and predicting possible equipment failures and damages, thereby allowing necessary maintenance measures to be taken to enhance equipment service life and reliability while reducing production costs and downtime. In recent years, PHM technology based on artificial intelligence (AI) has made remarkable achievements in the context of the industrial IoT and big data, and it is widely used in various industries, such as railway, energy, and aviation, for condition monitoring, fault prediction, and health management. The emergence of large-scale foundation models (LSF-Models) such as ChatGPT and DALLE-E marks the entry of AI into a new era of AI-2.0 from AI-1.0, where deep models have rapidly evolved from a research paradigm of single-modal, single-task, and limited-data to a multi-modal, multi-task, massive data, and super-large model paradigm. ChatGPT represents a landmark achievement in this research paradigm, offering hope for general artificial intelligence due to its highly intelligent natural language understanding ability. However, the PHM field lacks a consensus on how to respond to this significant change in the AI field, and a systematic review and roadmap is required to elucidate future development directions. To fill this gap, this paper systematically expounds on the key components and latest developments of LSF-Models. Then, we systematically answered how to build the LSF-Model applicable to PHM tasks and outlined the challenges and future development roadmaps for this research paradigm.