Pre-Whitening and BCJR Posterior Distillation for Bi-LSTM Detection in Faster-than-Nyquist Signaling

Faster-than-Nyquist signaling improves spectral ef- ficiency by deliberately introducing inter-symbol interference. Classical sequence detectors such as BCJR can approach optimal performance, but their computational cost grows rapidly with channel memory. This paper investigates data-driven FTN BPSK detection under AWGN through a direct comparison between multilayer perceptrons and Kolmogorov Arnold Networks. A large-scale Monte Carlo dataset containing nearly four million labeled windows is generated for a time-packing factor of zero point eight and signal-to-noise ratio values from seven to ten decibels. The best MLP obtained from width sweeping uses hidden width thirty two, whereas the selected KAN uses hidden width four with spline grid size five. At ten decibels, the MLP produces a bit error rate of one point three times ten to the minus four, while the KAN reaches seven times ten to the minus six. This corresponds to an eighteen point six times lower bit error rate while using only one eighth of the MLP hidden width. The results show that KAN provides a more effective and more parameter-efficient neural decision model than the MLP baseline for FTN BPSK detection.

Narrowband interference (NBI) severely degrades orthogonal frequency-division multiplexing (OFDM) systems by corrupting subcarriers and rendering classical soft demodulation ineffective. Conventional compressed-sensing (CS) mitigation exhibits high sequential latency and leaves structured, non-Gaussian residuals that cause log-likelihood ratio (LLR) unreliability, decoder saturation, and severe error floors when employing classical Gaussian demappers. We resolve this pipeline mismatch using a unified deep learning framework for joint NBI cancellation and robust soft demodulation. First, NBI-CNet employs a physics-informed convolutional architecture to estimate NBI parameters and remove multi-tone interference in a single forward pass. Without requiring prior knowledge of the active interferer count, NBI-CNet reduces computational complexity by up to 60% ($N{=}2048, Q{=}64$) compared to the state-of-the-art EOMP-IDS algorithm. Second, LLR-CNet acts as a structural whitener by mapping non-Gaussian post-mitigation residuals onto well-calibrated soft metrics. Simulations demonstrate that this joint framework eliminates the error floors inherent to traditional baselines across dense grids. Under severe interference ($\text{SIR}{=}{-}10$ dB), the pipeline operates within a $0.2$ to $0.5$ dB SNR margin of the optimal iterative baseline at a target block error rate (BLER) of $10^{-4}$. Under mild interference ($\text{SIR}{=}10$ dB) with heavy spectral overlap ($Q{=}12$), where classical greedy algorithms erroneously subtract valid data components and corrupt the payload, NBI-CNet avoids signal-peak confusion to deliver a coding gain exceeding $3$ dB. Finally, the architecture circumvents the $2{\times}10^{-4}$ error floor triggered by interferer-estimation errors, while its scale-invariant design enables robust generalization across arbitrary FFT sizes without retraining.

Trellis-coded quantization sets the current 2-bit post-training frontier for LLMs (QTIP), but pushing below the PTQ ceiling requires quantization-aware training, and QAT on a trellis is obstructed by the non-differentiable Viterbi argmax. We introduce BCJR-QAT, a relaxation that replaces the argmax with the BCJR forward-backward sum-product algorithm at temperature $T$, producing a soft codeword equal to the Boltzmann expectation over trellis paths, exactly differentiable, recovering the hard QTIP code as $T \to 0$, and mathematically identical to the transfer-matrix computation for a 1D Ising-like spin chain. We contribute (i) a fused Triton kernel making BCJR tractable on a single consumer GPU ($6.57\times$ speedup, fp32 parity); (ii) a quantitative drift-budget theory of when BCJR-QAT can escape the QTIP-PTQ Voronoi basin, verified across four experiments; and (iii) a positive empirical result on Llama-3.2-1B at 2 bpw under end-to-end forward-KL distillation: with the right schedule (skip the high-$T$ phase to avoid an overshoot we diagnose), single-layer BCJR-QAT beats QTIP-PTQ by $\mathbf{-0.084}$ PPL on WikiText-2, and multi-layer compounding is super-additive.