arXiv subjects

Xiaojing Yan

Publications and source records attributed to Xiaojing Yan.

5 recordsLinked to original sources

arXiv2025

Joint Bit-Partitioning and Modulation Design for Digital AirComp

For digital over-the-air computation, the ChannelComp framework has recently been proposed to design digital modulations to compute any arbitrary function over a multiple access channel. To reduce modulation design complexity while increasing computation reliability, this paper integrates a bit-partitioning procedure into ChannelComp. The key process is to partition the input bit sequence into several groups, map each group to a single modulation symbol and transmit the encoded symbol sequence across multiple time slots. With the objective to maximize a worst-case constellation distance, we develop two bit-partitioning methods. In uniform bit-partitioning, bits are evenly distributed across groups and modulation is designed via a max-min optimization, which is handled by a CCCP that solves a sequence of second-order cone programming subproblems. In importance-adaptive bit-partitioning (IABP), the bit allocation is adapted to the significance of individual bit positions, and the modulation and partitioning are jointly optimized. To keep the overall complexity manageable, simulated annealing is employed in the outer loop to update the partitioning, while a CCCP-based solver is used in the inner loop for modulation design. Numerical results show that both methods provide robust computation in noisy channels, and IABP achieves up to a 5 dB reduction in computation error compared to Sequential Modulation for AirComp, especially for product computation.

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arXiv2025

Multi-Symbol Digital AirComp via Modulation Design and Power Adaptation

Recently, over-the-air computation (AirComp) leverages the superposition property of wireless channels to enable efficient function computation over a multiple access channel (MAC). However, existing digital AirComp methods either rely on single-symbol modulation, which limits flexibility and robustness, or on multi-symbol extensions that suffer from high complexity or approximation errors. To overcome these limitations, we propose a new multi-symbol modulation framework, termed sequential modulation for AirComp (SeMAC), which encodes each input into a sequence of symbols with distinct constellation diagrams across multiple time slots. This approach increases design flexibility and robustness against channel noise. Specifically, the modulation design is formulated as a non-convex optimization problem and efficiently solved through a successive convex approximation (SCA) combined with stochastic subgradient descent (SSD). For fixed modulation formats, we further develop SeMAC with power adaptation (SeMAC-PA) to adjusts transmit power and phase while preserving the modulation structure. Notably, numerical results show that SeMAC improves computation accuracy by up to 14 dB compared to the existing methods for computing nonlinear functions such as the product function.

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arXiv2025

ReMAC:Digital Multiple Access Computing by Repeated Transmission

In this paper, we consider the ChannelComp framework, where multiple transmitters aim to compute a function of their values at a common receiver while using digital modulations over a multiple access channel. ChannelComp provides a general framework for computation by designing digital constellations for over-the-air computation. Currently, ChannelComp uses a symbol-level encoding. However, encoding repeated transmissions of the same symbol and performing the function computation using the corresponding received sequence may significantly improve the computation performance and reduce the encoding complexity. In this paper, we propose a new scheme where each transmitter repeats the transmission of the same symbol over multiple time slots while encoding such repetitions and designing constellation diagrams to minimize computational errors. We formally model such a scheme by an optimization problem, whose solution jointly identifies the constellation diagram and the repetition code. We call the proposed scheme ReMAC. To manage the computational complexity of the optimization, we divide it into two tractable subproblems. We verify the performance of ReMAC by numerical experiments. The simulation results reveal that ReMAC can reduce the computation error in noisy and fading channels by approximately up to 7.5$dB compared to standard ChannelComp, particularly for product functions.

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arXiv2024

A new fidelity of quantum channel evolution and its geometric interpretation

Fidelity is crucial for characterizing transformations of quantum states under various quantum channels, which can be served as a fundamental tool in resource theories. Firstly, we define an $\alpha$-$z$-fidelity as a significant quantity in quantum information theory and give the properties of the fidelity with orders $\alpha$ and $z$. Secondly, by analyzing the $\alpha$-$z$-fidelity under the evolution of different types of quantum channels (single orbit, all quantum channels, unitary quantum channels, and mixed unitary quantum channels), we propose a limit formula for the maximum and the minimum of the $\alpha$-$z$-fidelity. In addition, we have extended the $\alpha$-$z$-R\'enyi relative entropy, providing new insights into its relevance for resource quantification. Finally, we offer a geometric interpretation for measuring the distance between quantum states, contributing to the broader understanding of the operational and transformative power of dynamical quantum resources across various physical settings.

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arXiv2024

A Novel Channel Coding Scheme for Digital Multiple Access Computing

In this paper, we consider the ChannelComp framework, which facilitates the computation of desired functions by multiple transmitters over a common receiver using digital modulations across a multiple access channel. While ChannelComp currently offers a broad framework for computation by designing digital constellations for over-the-air computation and employing symbol-level encoding, encoding the repeated transmissions of the same symbol and using the corresponding received sequence may significantly improve the computation performance and reduce the encoding complexity. In this paper, we propose an enhancement involving the encoding of the repetitive transmission of the same symbol at each transmitter over multiple time slots and the design of constellation diagrams, with the aim of minimizing computational errors. We frame this enhancement as an optimization problem, which jointly identifies the constellation diagram and the channel code for repetition, which we call ReChCompCode. To manage the computational complexity of the optimization, we divide it into two tractable subproblems. Through numerical experiments, we evaluate the performance of ReChCompCode. The simulation results reveal that ReChCompCode can reduce the computation error by approximately up to 30 dB compared to standard ChannelComp, particularly for product functions.

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