[Paper Review] Analysis of Coded Selective-Repeat ARQ via Matrix Signal-Flow Graphs

Derya Malak, Muriel Médard+1 more|arXiv (Cornell University)|Jan 31, 2018

Cooperative Communication and Network Coding9 references3 citations

TL;DR

This paper proposes a coded selective-repeat ARQ protocol over packet erasure channels with unreliable feedback, using matrix signal-flow graphs (MSFGs) to model and analyze throughput and delay. It demonstrates that coded ARQ significantly reduces in-order delivery delay and maintains higher throughput than uncoded ARQ, especially at high block-error rates, due to effective error correction via MDS coding and feedback error resilience.

ABSTRACT

We propose two schemes for selective-repeat ARQ protocols over packet erasure channels with unreliable feedback: (i) a hybrid ARQ protocol with soft combining at the receiver, and (ii) a coded ARQ protocol, by building on the uncoded baseline scheme for ARQ, developed by Ausavapattanakun and Nosratinia. Our method leverages discrete-time queuing and coding theory to analyze the performance of the proposed data transmission methods. We incorporate forward error-correction to reduce in-order delivery delay, and exploit a matrix signal-flow graph approach to analyze the throughput and delay of the protocols. We demonstrate and contrast the performance of the coded protocols with that of the uncoded scheme, illustrating the benefits of coded transmissions.

Motivation & Objective

• To address the performance degradation of selective-repeat ARQ under unreliable feedback and high packet erasure rates in wireless networks.
• To reduce in-order delivery delay in ARQ protocols by integrating forward error correction (FEC) through coding techniques.
• To develop a rigorous analytical framework for throughput and delay in ARQ protocols with unreliable feedback using discrete-time queuing and coding theory.
• To compare the performance of coded ARQ against uncoded ARQ and HARQ with soft combining, focusing on efficiency and reliability trade-offs.
• To leverage matrix signal-flow graphs (MSFGs) for modeling complex feedback and erasure dynamics in ARQ systems with multiple states and error-prone feedback.

Proposed method

• Models the ARQ system using a Markov chain with states representing the number of decoded or acknowledged packets and feedback error states.
• Applies matrix signal-flow graphs (MSFGs) to represent the system as a set of linear equations, enabling the derivation of matrix-generating functions for transmission time and delay.
• Uses matrix-generating functions $\mathbf{\Phi}_{\tau}(z)$ and $\mathbf{\Phi}_{D}(z)$ to compute the moment generating functions of transmission and delay times, respectively.
• Incorporates transition probability matrices $\mathbf{P}_{ij}^{\rm C}(n)$ to model both forward channel erasures and feedback errors (e.g., erroneous ACK/NACK), with self-loops to model feedback retransmission states.
• Derives expressions for $A_n(z)$ and $B_n(z)$ to account for feedback error recovery and retransmission cycles, including the impact of cumulative feedback and decoding thresholds.
• Computes throughput $\eta$ as the inverse of average transmission time and average delay $\bar{D}$ from the first moments of the generating functions.

Experimental results

Research questions

• RQ1 How does the integration of MDS coding into selective-repeat ARQ improve throughput and delay performance under unreliable feedback?
• RQ2 What is the impact of feedback errors (e.g., misdecoded ACK/NACK) on the performance of ARQ protocols, and how can they be modeled effectively?
• RQ3 How does the coded ARQ scheme compare to uncoded ARQ and HARQ with soft combining in terms of delay and throughput across varying block-error rates?
• RQ4 To what extent can matrix signal-flow graphs (MSFGs) provide an analytical framework for modeling complex feedback and erasure dynamics in ARQ systems?
• RQ5 How does the system performance scale with timeout duration $T$, and what is the optimal trade-off between delay and throughput?

Key findings

• Coded ARQ achieves significantly lower average delay than uncoded ARQ, especially at high block-error rates ($\epsilon > 0.3$), due to effective error concealment via MDS coding.
• Throughput of the coded ARQ scheme decays more slowly with increasing $\epsilon$ compared to uncoded ARQ and HARQ with soft combining, indicating better resilience to channel errors.
• The HARQ scheme with soft combining provides a slight delay improvement over uncoded ARQ but offers similar throughput, indicating limited gains under the same feedback model.
• As timeout $T$ increases, both throughput and delay increase across all schemes, but the coded ARQ maintains superior performance margins at high $\epsilon$.
• The MSFG-based analytical model accurately captures the joint dynamics of forward channel erasures and feedback errors, enabling precise computation of throughput and delay metrics.
• The use of cumulative feedback and self-loops in the MSFG model effectively captures the retransmission behavior under feedback errors, improving model fidelity and predictive accuracy.