ARQ-based Average Consensus over Directed Network Topologies with Unreliable Communication Links

TL;DR

This work addresses discrete-time average consensus on strongly connected directed graphs with unreliable links. It introduces the (H)ARQ-RC algorithm by integrating (Hybrid) Automatic Repeat reQuest feedback into Robustified Ratio Consensus and augmenting the weight structure to account for delays and packet drops, establishing asymptotic convergence to the exact average $ar{x}=rac{1}{n}\sum_{i=1}^n x_i[0]$ with $z_j[k]=x_j[k]/y_j[k]$ approaching $ar{x}$. The authors prove almost-sure convergence using an augmented digraph that encodes delays via virtual nodes and packet drops via drop-recovery pathways, and they demonstrate, through extensive simulations, that the proposed method can achieve faster convergence and lower local buffering than the RC-RS approach while maintaining reliability. The solution supports practical deployment by enabling out-degree discovery through ACK feedback and by bounding information delays, offering a scalable, communication-efficient alternative for distributed estimation over unreliable networks. The work further discusses a trade-off between convergence speed and communication cost and points to future directions in adaptive retransmission policies guided by acknowledgement feedback and channel conditions.

Abstract

In this paper, we address the discrete-time average consensus problem in strongly connected directed graphs, where nodes exchange information over unreliable error-prone communication links. We enhance the Robustified Ratio Consensus algorithm by exploiting features of the (Hybrid) Automatic Repeat ReQuest - (H)ARQ protocol used for error control of data transmissions, in order to allow the nodes to reach asymptotic average consensus even when information is exchanged over error-prone directional networks. This strategy, apart from handling time-varying information delays induced by retransmissions of erroneous packets, can also handle packet drops that occur when exceeding a predefined packet retransmission limit. Invoking the (H)ARQ protocol allows nodes to: (a) exploit the incoming error-free acknowledgement feedback to initially acquire or later update their out-degree, (b) know whether a packet has arrived or not, and (c) determine a local upper-bound on the delays imposed by the retransmission limit. By augmenting the network's corresponding weight matrix, we show that nodes utilizing our proposed (H)ARQ Ratio Consensus algorithm can reach asymptotic average consensus over unreliable networks, while improving their convergence speed and maintaining low values in their local buffers compared to the current state-of-the-art.

Figures (13)

• Figure 1: (H)ARQ error control feedback mechanism.
• Figure 2: Packet error transition for a packet initially transmitted at iteration $k$ over the link $\varepsilon_{lj}$ with initial probability of error $q_{lj}$.
• Figure 3: An individual feedback signal ACK/NACK$f_{lj,k-r}[k]$ is sent from node $v_l$ for each packet $r=\{0,1,2\}$ it receives within each time slot. Black bullets denote a (re)transmission of packet $p_{lj} x_j [k-r]$; red and green bullets denote ACK and NACK, respectively; yellow bullets denote the iteration when node $v_{j}$ considers packets as dropped.
• Figure 4: Two node augmented digraph corresponding to the exchange of information through the (H)ARQ-RC algorithm. Yellow squares represent the virtual nodes due to retransmissions, while red squares represent the virtual nodes due to packet drops.
• Figure 5: Five node strongly-connected digraph.

Theorems & Definitions (9)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Theorem 1
• proof
• Lemma 1
• Lemma 2
• proof