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 — Fri, 17 Jul 2026 00:00:00 +0000

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.

Theoretical Study on Spatial Ring Formation and Stabilization of Spatiotemporal Solitons

V. Sabeer, N. K. Hashim, A. K. Shafeeque Ali — Sat, 11 Jul 2026 00:00:00 +0000

Spatiotemporal solitons become dynamically unstable in an unbalanced nonlinear medium. This study examines the conditions that enable stable propagation in both negative-index and positive-index regimes of metamaterials (MMs). Using Lagrangian variational analysis and the split-step Fourier method, we show that three-dimensional light bullets remain stable under specific conditions. In the negative-index regime, stability occurs when normal dispersion balances defocusing cubic and focusing quintic nonlinearities. In the positive-index regime, stability arises when anomalous dispersion interacts with focusing cubic and defocusing quintic nonlinearities. We also observe the formation of spatial rings during the propagation of a Gaussian beam in certain regimes of nonlinearity and dispersion. These results provide new insight into soliton dynamics in MMs and may enable applications in optical communications, photonics, and nonlinear optics.

Switching-Algebraic Evaluation of All-Terminal Reliability of a Computer-Communications Network: A Karnaugh-Map Perspective

Fri, 17 Jul 2026 00:00:00 +0000

Network reliability is a fundamental measure for assessing the ability of a network to maintain successful connectivity under component failures. In computer-communications networks, reliability evaluation depends on whether all nodes remain mutually connected despite edge failures. This paper presents a Boolean-based framework for evaluating the all-terminal reliability of bidirectional networks. Network success and failure are formulated as coherent switching functions of independent edge success indicators, and their probabilistic expectations are obtained through the Probability Transform after deriving probability-ready expressions. The proposed approach integrates path-set, spanning-tree, and cut-set methods within a unified switching-algebraic setting. The all-terminal success is expressed as the conjunction of selected two-terminal successes and, equivalently, as a disjunction of spanning trees, whereas the all-terminal failure is represented through a disjunction of vertex cut-sets. Regular Karnaugh maps are used to visualise coherence, absorption, complementation, prime implicants, and disjointness, while variable-entered Karnaugh maps are used to provide compact factored representations that preserve statistical independence and facilitate the derivation of probability-ready expressions. The methodology is demonstrated for a running example of a five-node, seven-edge network. For this example, the all-terminal success function comprises 21 spanning trees and is shellable, whereas the complementary failure function comprises only 10 vertex cut-sets and is non-shellable. The case of components with equal reliabilities is further examined through the derivation of reliability and unreliability polynomials, comparison with related k-out-of-n systems, and identification of the lower boundary of useful redundancy. The results indicate that Boolean algebra and Karnaugh-map techniques provide a transparent, pedagogical, and effective approach for network reliability computation and visualization.