In this paper, we investigate Kolmogorov-Arnold network-based autoencoders (KAN-AEs) with symbolic regression (SR) for energy-efficient channel coding. By using SR, we convert KAN-AEs into symbolic expressions, which enables low-complexity implementation and improved energy efficiency at the radios. To further enhance the efficiency, we introduce a new non-linearity score term in the SR process to help select lower-complexity equations when possible. Through numerical simulations, we demonstrate that KAN-AEs achieve competitive BLER performance while improving energy efficiency when paired with SR. We score the energy efficiency of a KAN-AE implementation using the proposed non-linearity metric and compare it to a multi-layer perceptron-based autoencoder (MLP-AE). Our experiment shows that the KAN-AE paired with SR uses 1.38 times less energy than the MLP-AE, supporting that KAN-AEs are a promising choice for energy-efficient deep learning-based channel coding.

In this study, we introduce smooshed binary modulation on conjugate-reciprocal zeros (SBMOCZ) to mitigate timing offset (TO)-induced zero rotation in binary modulation on conjugate-reciprocal zeros (BMOCZ)-based orthogonal frequency division multiplexing (OFDM). In our approach, we modify Huffman BMOCZ with zero smooshing to create a structured gap in the zero constellation which rotates under a TO. By exploiting the auto-correlation properties of SBMOCZ, we develop a low-complexity rotation estimator at the receiver that can be implemented using a single discrete Fourier transform (DFT). We theoretically analyze the properties of SBMOCZ polynomials and derive closed-form expressions for the aperiodic auto-correlation function (AACF) and peak-to-average power ratio (PAPR). To learn the smooshed zero constellation parameters, we introduce two machine learning (ML)-based methods. The first uses a soft-output from the direct zero-testing (DiZeT) decoder with hinge loss, while the second jointly trains a neural network (NN)-based decoder robust to fading and the constellation parameters. Our numerical simulations demonstrate that SBMOCZ remains effective under TO impairments without relying on affine cyclically permutable codes (ACPCs) and improves bit error rate (BER) and block error rate (BLER) at no additional overhead.

In this work, we propose jutted binary modulation on conjugate-reciprocal zeros (J-BMOCZ) for non-coherent communication under a carrier frequency offset (CFO). By introducing asymmetry to the Huffman BMOCZ zero constellation, we exploit the identical aperiodic auto-correlation function of BMOCZ sequences to derive a Fourier-domain metric for CFO estimation. Unlike the existing methods for Huffman BMOCZ, which require a cyclically permutable code (CPC) for pilot-free CFO correction, J-BMOCZ enables the estimation of a CFO without the use of pilots or channel coding. Through numerical simulations in additive white Gaussian noise and fading channels, we show that the bit error rate (BER) loss of J-BMOCZ under a CFO is just 1 dB over Huffman BMOCZ without a CFO. Furthermore, the results show that coded J-BMOCZ achieves better BER performance than Huffman BMOCZ with a CPC.

In this work, we propose two methods to design zero constellations for binary modulation on conjugate-reciprocal zeros (BMOCZ). In the first approach, we treat constellation design as a multi-label binary classification problem and learn the zero locations for a direct zero-testing (DiZeT) decoder. In the second approach, we introduce a neural network (NN)-based decoder and jointly learn the decoder and zero constellation parameters. We show that the NN-based decoder can directly generalize to flat-fading channels, despite being trained under additive white Gaussian noise. Furthermore, the results of numerical simulations demonstrate that learned zero constellations outperform the canonical, Huffman BMOCZ constellation, with the proposed NN-based decoder achieving large performance gain at the expense of increased computational complexity.

In this study, we propose a new binary modulation on conjugate-reciprocal zeros (BMOCZ) zero constellation, which we call smooshed binary modulation on conjugate-reciprocal zeros (SBMOCZ), to address carrier frequency offset (CFO)induced zero rotation without depending on channel coding. In our approach, we modify the phase mapping of Huffman BMOCZ by shrinking the angle between adjacent zeros, except for the first and last, to introduce a gap in the zero constellation. By discerning the gap location in the received polynomial, the receiver can estimate and correct the phase rotation. We demonstrate the error rate performance of SBMOCZ relative to Huffman BMOCZ, showing that SBMOCZ addresses a CFO-induced rotation at the cost of a modest performance reduction compared to Huffman BMOCZ in the absence of a CFO. Finally, we compare SBMOCZ to Huffman BMOCZ using a cyclically permutable code (CPC), showing a 4 dB bit error rate (BER) improvement in a fading channel, while demonstrating comparable performance across other simulations.