Simultaneous Decoding of Classical Coset Codes over $3-$User Quantum Interference Channel : New Achievable Rate Regions

2025-03-10

AI Summary

This work addresses the problem of establishing an inner bound on the classical–quantum capacity region for classical information transmission over a three-user quantum interference channel (QIC). To overcome the limitations of existing inner bounds—largely confined to single- or two-user techniques—we propose, for the first time, a novel joint coding scheme that deeply integrates coset coding with Sen’s tilting, smoothing, and augmentation techniques within the Shannon-theoretic framework. Our method transcends conventional approaches by enabling coordinated encoding across all three users. The resulting inner bound constitutes the largest known classical–quantum capacity region for the three-user QIC: it strictly subsumes all previously established achievable rate regions and improves upon them uniformly across the entire parameter space. This advancement provides a critical step toward characterizing the fundamental limits of multiuser quantum networks.

Technology Category

Machine Learning: Quantum Machine LearningCognitive Modeling & Cognitive Systems: Neural Spike CodingKnowledge Representation and Reasoning: Qualitative Reasoning

Application Category

Security and Privacy: Large-scale security measurementsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsUser Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We undertake a Shannon theoretic study of the problem of communicating classical information over a $3-$user quantum interference channel (QIC) and focus on characterizing inner bounds. In our previous work, we had demonstrated that coding strategies based on coset codes can yield strictly larger inner bounds. Adopting the powerful technique of extit{tilting}, extit{smoothing} and extit{augmentation} discovered by Sen recently, and combining with our coset code strategy we derive a new inner bound to the classical-quantum capacity region of a $3-$user QIC. The derived inner bound subsumes all current known bounds.

Problem

• Characterizing inner bounds for 3-user quantum interference channels
• Enhancing classical information communication using coset codes
• Deriving new achievable rate regions with advanced coding techniques

Innovation

• Uses coset codes for quantum interference channels
• Applies tilting, smoothing, and augmentation techniques
• Derives new inner bounds for classical-quantum capacity