Coded Fourier-Curve Constellations with Tangent Artificial Noise: Covariance-Aware Demapping, Complexity, and Key Sensitivity

Abstract

We realize and evaluate the covariance-aware soft demapper for a coded link over phase-keyed Fourier-curve constellations with tangent artificial noise (AN). A phase key shared by transmitter and legitimate receiver instantiates a codebook of $M$ points on a closed curve through $k$ complex slots; AN along the curve's tangent gives every symbol a Gaussian observation with a symbol-dependent rank-one covariance. The maximum-likelihood symbol metric then differs from the Euclidean rule by one rank-one correction per candidate, realized as a max-log demapper beside a Euclidean matched-filter bank at $2kM$ extra multiply--accumulate operations per symbol and a $10$\,KB lookup table. On a regular $(3,6)$ LDPC-coded link at $(k,M){=}(20,64)$ it reaches BLER${=}10^{-1}$ about $5$\,dB earlier than Euclidean demapping under natural labeling and $1.0$\,dB earlier under Gray labeling, the better labeling for both; whitening only the average AN covariance recovers $0.7$\,dB of the natural-labeling gap, the rest being due to the candidate-specific covariance label. A bit-interleaved coded-modulation achievable-rate computation corroborates the ordering, a Woodbury extension keeps the rank-one structure under per-tone Ricean fading, and $6$-bit lookup-table quantization costs no measurable coded-BLER degradation. Finally, the key is a modulation parameter rather than a secret: decoding needs a per-component key accuracy of about $0.5$\,rad, and a design-aware receiver recovers it to within $0.1$\,rad from the third-order moments of a single LDPC block, decoding at the legitimate receiver's level, so we make no secrecy claim.