[Paper Review] Delay-Energy lower bound on Two-Way Relay Wireless Network Coding

Hongyi Zeng, Wei Chen|arXiv (Cornell University)|Jan 24, 2014

Cooperative Communication and Network Coding6 references3 citations

TL;DR

This paper proposes Enhanced Network Coding (ENC), a continuous-time network coding scheme that transmits both coded and uncoded packets to minimize delay and eliminate packet loss in two-way relay wireless networks. By modeling the relay as a Markov process and solving a linear programming problem, ENC achieves the theoretical lower bound on the delay-energy trade-off, outperforming conventional network coding under finite buffer constraints.

ABSTRACT

Network coding is a novel solution that significantly improve the throughput and energy consumed of wireless networks by mixing traffic flows through algebraic operations. In conventional network coding scheme, a packet has to wait for packets from other sources to be coded before transmitting. The wait-and-code scheme will naturally result in packet loss rate in a finite buffer. We will propose Enhanced Network Coding (ENC), an extension to ONC in continuous time domain. In ENC, the relay transmits both coded and uncoded packets to reduce delay. In exchange, more energy is consumed in transmitting uncoded packets. ENC is a practical algorithm to achieve minimal average delay and zero packet-loss rate under given energy constraint. The system model for ENC on a general renewal process queuing is presented. In particular, we will show that there exists a fundamental trade-off between average delay and energy. We will also present the analytic result of lower bound for this trade-off curve, which can be achieved by ENC.

Motivation & Objective

• To address the inherent packet loss in conventional network coding due to finite buffer constraints in wireless relay networks.
• To model and analyze the delay-energy trade-off in continuous-time two-way relay networks using renewal and Poisson processes.
• To develop a practical network coding scheme that achieves minimal average delay and zero packet loss under a given energy budget.
• To derive the theoretical lower bound of the delay-energy trade-off curve and validate it through simulation.
• To demonstrate that first-come-first-serve policies are insufficient for minimizing delay, necessitating adaptive transmission strategies.

Proposed method

• Extends Opportunistic Network Coding (ONC) from discrete to continuous time domain, introducing Enhanced Network Coding (ENC) for general renewal processes and Poisson arrivals.
• Models the relay queue as a continuous-time Markov chain with states representing the number of stored packets, using transition rates $ f_k $ and $ g_k $ for transmission decisions.
• Introduces a hybrid transmission policy: immediate coded transmission when both queues are non-empty, and probabilistic uncoded transmission when one queue is empty.
• Derives analytical expressions for average delay, packet-loss rate $ heta $, and average energy consumption $ ar{E} $, based on stationary distribution $ oldsymbol{ ho}^* $.
• Reformulates the delay-energy optimization as a linear programming problem to find the optimal transmission policy $ f_k^* $ and $ g_k^* $ under energy constraints.
• Validates theoretical results via an event-driven Monte Carlo simulator in C++ for Poisson and renewal processes.

Experimental results

Research questions

• RQ1 What is the fundamental trade-off between average delay and energy consumption in two-way relay wireless networks with finite buffers?
• RQ2 Can a continuous-time network coding scheme eliminate packet loss while minimizing delay under energy constraints?
• RQ3 How does the performance of conventional network coding degrade under finite buffer conditions, and what is the achievable lower bound on delay-energy trade-off?
• RQ4 What transmission policy (coded vs. uncoded) optimally balances delay and energy consumption in a Markovian relay queue?
• RQ5 Under what energy constraints does the system achieve zero delay, and when does delay become infinite due to insufficient energy?

Key findings

• Conventional network coding with finite buffers inevitably results in non-zero packet loss, with normalized loss rate $ heta = rac{1}{1+2K} $ when $ g_K = 0 $, where $ K $ is buffer size.
• ENC achieves the theoretical lower bound on the delay-energy trade-off curve, with optimal performance derived via linear programming and validated by simulation.
• The optimal delay is a decreasing, piecewise linear function of the minimal energy constraint $ ar{E}_{ ext{max}} $, with $ K $ linear segments for buffer size $ K $.
• When $ ar{E}_{ ext{max}} > 2 $, delay is zero, indicating immediate transmission without queuing; when $ ar{E}_{ ext{max}} < 1 + rac{1}{1+2K} hickapprox 1.143 $, delay becomes infinite due to insufficient energy.
• For $ ar{E}_{ ext{max}} = 1 + rac{1}{1+2m} + ar{ ho} $ with $ ar{ ho} o 0^+ $, the optimal policy simplifies: $ f_k^* o 0 $ and $ k^* = m $, indicating a minimal transmission strategy.
• Simulation results perfectly match the theoretical trade-off curve, confirming the accuracy of the Markov model and the optimality of the derived ENC policy.