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Journal of Advances in Mathematics and Computer Science

A Unified Quantum–Classical Framework for BER Analysis of Different Modulations under AWGN and Fading Channels

Aahana Nischal, Arav Jha, Nikhilesh Rao, R. Bhagya, K. Saraswathi

Published Jul 17, 2026• 0 citations
Publisher

Abstract

Reliable communication under additive noise, multipath fading, and mobility-induced channel variation remains a central requirement in contemporary wireless systems. This study develops a unified quantum-classical framework for examining bit error rate (BER) performance across ideal and impaired channel conditions. The classical component models orthogonal frequency-division multiplexing with BPSK, QPSK, 8-PSK, and 4-, 16-, 64-, and 128-QAM using MATLAB R2026a. The quantum-proxy component is implemented in Qiskit 2.3.0 using computational-basis qubits and Kraus-operator models for bit-flip, amplitude-damping, and phase damping noise. BER is evaluated against signal-to-noise ratio (SNR) for additive white Gaussian noise and combined fading and Doppler conditions. The classical results show a consistent reduction in BER as SNR increases, with BPSK exhibiting the greatest robustness and higher-order PSK and QAM schemes showing greater sensitivity to channel impairment. In the quantum-proxy simulation, BER remains largely independent of the number of bits represented per symbol because each qubit is encoded and measured as an independent binary state. Phase damping has negligible influence on computational-basis measurement outcomes, whereas bit-flip and amplitude-damping processes principally determine the observed errors. The numerical BER values from the two frameworks are not directly comparable because the quantum SNR axis represents a proxy mapping to noise probabilities rather than a calibrated physical Eb/N0 measure. The framework therefore supports a qualitative comparison of error mechanisms while clarifying the present limitations of basis-state quantum encoding for modelling higher-order modulation.

DOI
10.9734/jamcs/2026/v41i82185

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Reliable communication under additive noise, multipath fading, and mobility-induced channel variation remains a central requirement in contemporary wireless systems. This study develops a unified quantum-classical framework for examining bit error rate (BER) performance across ideal and impaired channel conditions. The classical component models orthogonal frequency-division multiplexing with BPSK, QPSK, 8-PSK, and 4-, 16-, 64-, and 128-QAM using MATLAB R2026a. The quantum-proxy component is implemented in Qiskit 2.3.0 using computational-basis qubits and Kraus-operator models for bit-flip, amplitude-damping, and phase damping noise. BER is evaluated against signal-to-noise ratio (SNR) for additive white Gaussian noise and combined fading and Doppler conditions. The classical results show a consistent reduction in BER as SNR increases, with BPSK exhibiting the greatest robustness and higher-order PSK and QAM schemes showing greater sensitivity to channel impairment. In the quantum-proxy simulation, BER remains largely independent of the number of bits represented per symbol because each qubit is encoded and measured as an independent binary state. Phase damping has negligible influence on computational-basis measurement outcomes, whereas bit-flip and amplitude-damping processes principally determine the observed errors. The numerical BER values from the two frameworks are not directly comparable because the quantum SNR axis represents a proxy mapping to noise probabilities rather than a calibrated physical Eb/N0 measure. The framework therefore supports a qualitative comparison of error mechanisms while clarifying the present limitations of basis-state quantum encoding for modelling higher-order modulation.
Quantum communication leverages fundamental principles of quantum mechanics, such as superposition and measurement-induced disturbance, to enable robust information transfer under noisy conditions. In this work, a novel quantum-inspired communication framework for continuous-valued audio signal transmission is proposed and evaluated through classical simulation. The system employs Single-Qubit Probability Amplitude Modulation (SQPAM) to preserve amplitude continuity and integrates a three-qubit Quantum Inspired Error Correction scheme to mitigate channel-induced bit-flip errors, while channel impairments are modeled using a Monte Carlo–based Depolarizing noise process for controlled evaluation across varying noise levels. At the receiver, majority-voting decoding followed by inverse SQPAM mapping reconstructs the transmitted audio signal. Performance evaluation using objective reconstruction measures, perceptual quality metrics, and quantum-domain fidelity analysis demonstrates significant improvements over non-error-corrected and classical repetition-based baselines, achieving STOI values up to 0.9984 and providing an effective SNR advantage of approximately 2–3 dB, thereby highlighting the robustness and practical potential of the proposed framework for high-fidelity audio transmission in noise-limited environments.
Quantum dense coding enables the transmission of two classical bits of information through the exchange of a single qubit, provided that an entangled state is shared between the communicating parties. While this protocol achieves a fundamental increase in channel capacity, its practical realization is strongly influenced by the presence of noise in realistic quantum channels. This work presents a simulation-based study of dense coding performance under two representative noise models: the depolarizing channel and the amplitude damping channel. Using Qiskit Aer, the bit error rate (BER), frame error rate (FER), and effective channel capacity are evaluated across a range of noise parameters. In addition, a classical threefold repetition strategy is examined as a lightweight error-mitigation technique. Results indicate that depolarizing noise produces more rapid degradation in both BER and channel capacity compared to amplitude damping, while repetition coding provides partial improvement in reliability at the expense of resource overhead. These findings highlight the trade-offs between efficiency and robustness in noisy implementations of dense coding and motivate further exploration of more advanced quantum error correction methods.
The rapid growth of next-generation networks has created a strong demand for communication systems that have delivered high reliability, low latency, and resilience under harsh channel conditions. Although classical error correction codes have improved many wireless links, their performance has proved insufficient as data rates increased and channel dynamics became more unpredictable. This study has explored a quantum-inspired error correction framework that has combined structural principles from quantum stabilizer codes with the efficiency of classical block codes. The aim was to provide an adaptive mechanism that has reduced noise effects and supported ultra-reliable communication targets. The problem has emerged from the gap between existing coding techniques and the reliability requirements of mission-critical services. Classical codes have struggled when the channel has exhibited fast fading or burst noise, and quantum codes, while powerful, have required complex hardware. The proposed approach has addressed this gap by adopting quantum-inspired parity structures that have retained the lightweight processing of classical codes while mimicking the robustness observed in quantum systems. The method has employed a hybrid coding model that has integrated a modified stabilizer-like generator with a classical low-density parity check backbone. The encoder has produced redundant qubit-analogous syndromes that have allowed the decoder to infer error patterns with higher confidence. A sequential belief-propagation algorithm has been used, which has adjusted decoding weights according to channel variation. Simulations have been performed over Rayleigh and Rician channels, and the system has been tested under high mobility. The results of the proposed framework demonstrate substantial improvements over conventional coding methods. The hybrid stabilizer-LDPC structure reduces the bit error rate from 22.3% to 0.5% across an SNR range of 0–20 dB and lowers the frame error rate from 45.7% to 1.1%. Throughput improves from 4.2 Mbps at 0 dB to 13.8 Mbps at 20 dB, while the average decoding iterations decrease from 42 to 5, indicating reduced computational complexity. Under high-speed mobility, BER and FER remain low at 2.3% and 4.6%, respectively, while throughput stays above 10.2 Mbps and convergence requires only 12 iterations. These numerical results confirm that the proposed method provides highly reliable, efficient, and adaptive error correction suitable for next-generation networks.
Quantum communication stands on the precipice of a transformative leap with the advent of Quantum Orthogonal Frequency Division Multiplexing (Q-OFDM). Drawing from the classical OFDM paradigm, Q-OFDM utilizes the Quantum Fourier Transform (QFT) and its inverse (IQFT) for high-fidelity information encoding and decoding across quantum channels. This study presents a novel Q-OFDM communication model that utilizes quantum superposition and entanglement to distribute data over many orthogonal quantum states, like frequency channels in conventional OFDM. Using the Qiskit platform, we meticulously analyze the bit error rate (BER) across various quantum rotations—Rx, Ry, and Rz—focusing on the rotation anglesθ={20,50,100}\boldsymbol{\theta}=\{\mathbf{20},\mathbf{50},\mathbf{100}\}θ={20,50,100}degrees. Our simulations reveal critical insights into the BER behavior in response to quantum gate operations, with larger qubit counts showing intrinsic error reduction. Accentuating the Q-OFDM system's robustness against quantum noise and operational errors.
Quantum communication offers a promising solution to overcome the limitations of classical communication, especially in addressing channel noise and signal fading. Inspired by classical Orthogonal Frequency Division Multiplexing (OFDM), this study introduces a novel Quantum OFDM (QOFDM) framework for image transmission over noisy quantum channels. In the proposed system, the input image bitstream is channel encoded and then quantum encoded using qubit sizes ranging from 1 to 8, optimizing the trade-off between complexity and performance. This data is processed via serial-to-parallel conversion, and the Quantum Fourier Transform (QFT) is applied to create orthogonal subcarriers. After reconversion to serial, a cyclic prefix is added to mitigate inter-symbol interference. At the receiver, the cyclic prefix is removed, the signal is converted to parallel, and Inverse QFT (IQFT) is applied to recover the quantum states. The system then performs parallel-to-serial conversion, quantum decoding, and classical reconstruction to retrieve the transmitted image. Performance evaluation using Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) shows that QOFDM outperforms classical OFDM in both image quality and noise resilience. The eight-qubit configuration achieves notable channel Signal-to-Noise Ratio (SNR) gains, 22 dB in urban environments, and 16 dB in indoor settings over classical BPSK, despite higher computational demands. These results demonstrate the significant potential of QOFDM to improve multimedia communications.
Reliable transmission of compressed images over error-prone channels remains challenging because compressed bitstreams are highly sensitive to channel impairments. Although existing quantum-inspired encoding schemes exploit superposition to improve transmission reliability, they remain vulnerable to channel noise, limiting reconstructed image quality. To address these limitations, this paper proposes a chirp transform-based multi-qubit encoding framework for robust compressed image transmission. Unlike conventional transform-based approaches, including the Hadamard transform and Quantum Fourier Transform (QFT), the proposed framework introduces nonlinear (quadratic) phase modulation into the multi-qubit representation, producing a high-dimensional superposition that enhances noise resilience through improved phase separability. This nonlinear phase variation improves error resilience through phase-induced decorrelation, reducing noise-induced distortions. The system integrates Joint Photographic Experts Group (JPEG) and High Efficiency Image File Format (HEIF) source encoding, followed by channel coding, multi-qubit encoding, and chirp transformation before transmission through a simulated quantum channel. At the receiver, inverse chirp transformation, measurement-based decoding, channel decoding, and source decoding reconstruct the transmitted image. Performance is evaluated using Bit Error Rate (BER), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Universal Quality Index (UQI). Experimental results demonstrate that the proposed framework achieves up to a 3 dB signal-to-noise ratio (SNR) gain over QFT-based and Hadamard-based systems in the single-qubit configuration. For the eight-qubit configuration, gains of up to 2 dB over QFT-based systems and 7 dB over Hadamard-based systems are achieved. These results demonstrate the effectiveness and scalability of the proposed framework for robust compressed image transmission over noisy quantum communication channels.