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Hypergame Theory for Decentralized Resource Allocation in Multi-user Semantic Communications

Christo Kurisummoottil Thomas, Walid Saad

TL;DR

Simulation results show that the proposed Stackelberg hypergame results in efficient usage of communication and computing resources while maintaining a high quality of experience for the users compared to state-of-the-art that does not account for the misperceptions.

Abstract

Semantic communications (SC) is an emerging communication paradigm in which wireless devices can send only relevant information from a source of data while relying on computing resources to regenerate missing data points. However, the design of a multi-user SC system becomes more challenging because of the computing and communication overhead required for coordination. Existing solutions for learning the semantic language and performing resource allocation often fail to capture the computing and communication tradeoffs involved in multiuser SC. To address this gap, a novel framework for decentralized computing and communication resource allocation in multiuser SC systems is proposed. The challenge of efficiently allocating communication and computing resources (for reasoning) in a decentralized manner to maximize the quality of task experience for the end users is addressed through the application of Stackelberg hyper game theory. Leveraging the concept of second-level hyper games, novel analytical formulations are developed to model misperceptions of the users about each other's communication and control strategies. Further, equilibrium analysis of the learned resource allocation protocols examines the convergence of the computing and communication strategies to a local Stackelberg equilibria, considering misperceptions. Simulation results show that the proposed Stackelberg hyper game results in efficient usage of communication and computing resources while maintaining a high quality of experience for the users compared to state-of-the-art that does not account for the misperceptions.

Hypergame Theory for Decentralized Resource Allocation in Multi-user Semantic Communications

TL;DR

Simulation results show that the proposed Stackelberg hypergame results in efficient usage of communication and computing resources while maintaining a high quality of experience for the users compared to state-of-the-art that does not account for the misperceptions.

Abstract

Semantic communications (SC) is an emerging communication paradigm in which wireless devices can send only relevant information from a source of data while relying on computing resources to regenerate missing data points. However, the design of a multi-user SC system becomes more challenging because of the computing and communication overhead required for coordination. Existing solutions for learning the semantic language and performing resource allocation often fail to capture the computing and communication tradeoffs involved in multiuser SC. To address this gap, a novel framework for decentralized computing and communication resource allocation in multiuser SC systems is proposed. The challenge of efficiently allocating communication and computing resources (for reasoning) in a decentralized manner to maximize the quality of task experience for the end users is addressed through the application of Stackelberg hyper game theory. Leveraging the concept of second-level hyper games, novel analytical formulations are developed to model misperceptions of the users about each other's communication and control strategies. Further, equilibrium analysis of the learned resource allocation protocols examines the convergence of the computing and communication strategies to a local Stackelberg equilibria, considering misperceptions. Simulation results show that the proposed Stackelberg hyper game results in efficient usage of communication and computing resources while maintaining a high quality of experience for the users compared to state-of-the-art that does not account for the misperceptions.
Paper Structure (20 sections, 6 theorems, 23 equations, 3 figures)

This paper contains 20 sections, 6 theorems, 23 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. System Model
  5. Semantics Reasoning Model
  6. Computing Model
  7. Hypergame Formulation for Communication and Computing Resource Allocation
  8. Utility Functions
  9. Hypergame Theory for Handling Misperceptions
  10. Equilibrium Analysis
  11. Proposed alternating minimization solution
  12. TX and RX strategy updates
  13. Perception updates for two-user system
  14. Convergence of the proposed solution
  15. Simulation Results and Analysis
  16. ...and 5 more sections

Key Result

Lemma 1

The reasoning success probability $P(\tau_{kj} \leq \tau^{\mathrm{max}})$ for Gaussian distributions $p(\widehat{c}_{kr}^{(j)}\mid c_{kr})$ is upper bounded by $e^{-\frac{x_{kj}^2}{2}}$, where $x_{kj}\! = \! \frac{N_0B(\!2^{\frac{\beta_{kj}(2)}{B(\tau^{\mathrm{max}} - \beta_{kj}(1))}} \!-\! 1)}{P_i\

Figures (3)

  • Figure 1: RX utility as a function of the number of game iterations.
  • Figure 2: Number of bits transmitted vs function of Tx perception error.
  • Figure 3: Number of bits communicated vs semantic relevance, for a fixed QoTE and $\tau^{\mathrm{max}}$.

Theorems & Definitions (8)

  • Lemma 1
  • Definition 1: Second level hypergame
  • Definition 2: Hyper Stackelberg Equilibrium, HSE
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Theorem 1