Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An Information-Theoretic Efficient Capacity Region for Multi-User Interference Channel

Sagnik Bhattacharya, Abhiram Rao Gorle, Muhammad Ali Mohsin, John M. Cioffi

TL;DR

This work addresses the capacity region of multi-user interference channels (IC) where each user encodes $U$ sub-user components. It develops a unified, $EPI$-based framework showing that Gaussian signaling at the sub-user level is optimal and constructs a finite, explicit IC capacity region under a sum-power constraint via a partial-MAC formulation that avoids auxiliary random variables. By decoupling decoding-order search from power allocation through a Lagrangian approach and time-sharing, it enables efficient minimum-sum-power optimization with near-optimal performance, outperforming OMA in simulations. The resulting convex capacity region and scalable optimization pathway offer a practical, interference-aware design paradigm for next-generation, cell-free wireless networks with reduced overhead and improved energy efficiency.

Abstract

We investigate the capacity region of multi-user interference channels (IC), where each user encodes multiple sub-user components. By unifying chain-rule decomposition with the Entropy Power Inequality (EPI), we reason that single-user Gaussian codebooks suffice to achieve optimal performance, thus obviating any need for intricate auxiliary variables or joint typicality arguments. Our partial-MAC formulation enumerates sub-user decoding orders while only imposing constraints for sub-users actually decoded. This significantly reduces complexity relative to enumerating all subsets or bruteforcing over all successive interference cancellation (SIC) decoding order combinations at all receivers. This leads to a finite but comprehensive construction of all achievable rate tuples under sum-power constraints, while guaranteeing that each receiver fully recovers its intended sub-user signals. Consequently, known single-user Gaussian capacity results generalize naturally to multi-user scenarios, revealing a cohesive framework for analyzing multi-user IC. Our results thus offer a streamlined, tractable pathway for designing next-generation cell-free wireless networks that rely on IC mechanisms, efficiently exploiting interference structure while minimizing overhead. Overall, this provides a unifying perspective.

An Information-Theoretic Efficient Capacity Region for Multi-User Interference Channel

TL;DR

This work addresses the capacity region of multi-user interference channels (IC) where each user encodes sub-user components. It develops a unified, -based framework showing that Gaussian signaling at the sub-user level is optimal and constructs a finite, explicit IC capacity region under a sum-power constraint via a partial-MAC formulation that avoids auxiliary random variables. By decoupling decoding-order search from power allocation through a Lagrangian approach and time-sharing, it enables efficient minimum-sum-power optimization with near-optimal performance, outperforming OMA in simulations. The resulting convex capacity region and scalable optimization pathway offer a practical, interference-aware design paradigm for next-generation, cell-free wireless networks with reduced overhead and improved energy efficiency.

Abstract

We investigate the capacity region of multi-user interference channels (IC), where each user encodes multiple sub-user components. By unifying chain-rule decomposition with the Entropy Power Inequality (EPI), we reason that single-user Gaussian codebooks suffice to achieve optimal performance, thus obviating any need for intricate auxiliary variables or joint typicality arguments. Our partial-MAC formulation enumerates sub-user decoding orders while only imposing constraints for sub-users actually decoded. This significantly reduces complexity relative to enumerating all subsets or bruteforcing over all successive interference cancellation (SIC) decoding order combinations at all receivers. This leads to a finite but comprehensive construction of all achievable rate tuples under sum-power constraints, while guaranteeing that each receiver fully recovers its intended sub-user signals. Consequently, known single-user Gaussian capacity results generalize naturally to multi-user scenarios, revealing a cohesive framework for analyzing multi-user IC. Our results thus offer a streamlined, tractable pathway for designing next-generation cell-free wireless networks that rely on IC mechanisms, efficiently exploiting interference structure while minimizing overhead. Overall, this provides a unifying perspective.
Paper Structure (34 sections, 35 equations, 2 figures)

This paper contains 34 sections, 35 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Multi-user Interference Channel
  3. Sub-User Components and Decoding Orders
  4. Comparison with MAC and BC Channels
  5. Challenges in IC Capacity Region Characterization
  6. Power Minimization Under Rate Constraints
  7. Gaussian assumption on sub-user components
  8. Strengthened Versions of the EPI
  9. Proof of the EPI: A Differential Entropy Approach
  10. Proof of the EPI: Forney’s Crypto Lemma and Mixing
  11. Implications for Gaussianity and Mixing
  12. Optimality of Gaussian Inputs
  13. Reduction of Optimization Complexity
  14. Interference Channel Capacity Region
  15. Capacity Region Derivation
  16. ...and 19 more sections

Figures (2)

  • Figure 1: A 2-user interference channel
  • Figure 2: Comparison with OMA