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HARQ-based Quantized Average Consensus over Unreliable Directed Network Topologies

Neofytos Charalampous, Evagoras Makridis, Apostolos I. Rikos, Themistoklis Charalambous

TL;DR

This work addresses quantized average consensus over directed graphs with unreliable links by introducing HARQ-QAC, a distributed algorithm that leverages ARQ feedback channels and retransmissions to cope with packet drops. Nodes maintain mass-tracking variables and run a round-robin transmission scheme, with event-triggered updates (C1 and C2) guiding finite-time, exact convergence to the average $\hat{y} = \frac{\sum_{v_i} y_i[0]}{n}$ in the presence of losses. The main contributions include a provably finite-time, almost-sure convergence guarantee for quantized communication on directed graphs with HARQ, demonstrated via an illustrative example and simulations showing acceleration when retransmissions are enabled (smaller $\lambda$). The results offer robust, bandwidth-efficient distributed averaging suitable for wireless sensor networks and IoT where links are unreliable and quantized data is essential.

Abstract

In this paper, we propose a distributed algorithm (herein called HARQ-QAC) that enables nodes to calculate the average of their initial states by exchanging quantized messages over a directed communication network. In our setting, we assume that our communication network consists of unreliable communication links (i.e., links suffering from packet drops). For countering link unreliability our algorithm leverages narrowband error-free feedback channels for acknowledging whether a packet transmission between nodes was successful. Additionally, we show that the feedback channels play a crucial role in enabling our algorithm to exhibit finite-time convergence. We analyze our algorithm and demonstrate its operation via an example, where we illustrate its operational advantages. Finally, simulations corroborate that our proposed algorithm converges to the average of the initial quantized values in a finite number of steps, despite the packet losses. This is the first quantized consensus algorithm in the literature that can handle packet losses and converge to the average. Additionally, the use of the retransmission mechanism allows for accelerating the convergence.

HARQ-based Quantized Average Consensus over Unreliable Directed Network Topologies

TL;DR

This work addresses quantized average consensus over directed graphs with unreliable links by introducing HARQ-QAC, a distributed algorithm that leverages ARQ feedback channels and retransmissions to cope with packet drops. Nodes maintain mass-tracking variables and run a round-robin transmission scheme, with event-triggered updates (C1 and C2) guiding finite-time, exact convergence to the average in the presence of losses. The main contributions include a provably finite-time, almost-sure convergence guarantee for quantized communication on directed graphs with HARQ, demonstrated via an illustrative example and simulations showing acceleration when retransmissions are enabled (smaller ). The results offer robust, bandwidth-efficient distributed averaging suitable for wireless sensor networks and IoT where links are unreliable and quantized data is essential.

Abstract

In this paper, we propose a distributed algorithm (herein called HARQ-QAC) that enables nodes to calculate the average of their initial states by exchanging quantized messages over a directed communication network. In our setting, we assume that our communication network consists of unreliable communication links (i.e., links suffering from packet drops). For countering link unreliability our algorithm leverages narrowband error-free feedback channels for acknowledging whether a packet transmission between nodes was successful. Additionally, we show that the feedback channels play a crucial role in enabling our algorithm to exhibit finite-time convergence. We analyze our algorithm and demonstrate its operation via an example, where we illustrate its operational advantages. Finally, simulations corroborate that our proposed algorithm converges to the average of the initial quantized values in a finite number of steps, despite the packet losses. This is the first quantized consensus algorithm in the literature that can handle packet losses and converge to the average. Additionally, the use of the retransmission mechanism allows for accelerating the convergence.

Paper Structure

This paper contains 6 sections, 1 theorem, 4 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. Problem Formulation
  4. Main Results
  5. Simulation Results
  6. Conclusions and Future Directions

Key Result

Proposition 1

Consider a strongly connected digraph $\mathcal{G}_d =(\mathcal{V}, \mathcal{E})$ with $n=|\mathcal{V}|$ nodes and $m=|\mathcal{E}|$ edges. Suppose that each node $v_j\in\mathcal{V}$ executes Algorithm alg:arq_quantized. Then, we can find a finite number of steps $k_1\in\mathds{N}$, such that for $k almost surely (i.e., with probability 1).

Figures (4)

  • Figure 1: The digraph considered in Example 1 (left), along with its associated feedback links (right).
  • Figure 2: Ratio of $v_i\in\mathcal{V}$. Upper: SC1, middle: SC2, and lower: SC3.
  • Figure 3: Average consensus error for the three considered scenarios.
  • Figure 4: Convergence for error rates 60% and 80%

Theorems & Definitions (3)

  • Remark 1
  • Proposition 1
  • proof