[Paper Review] Benefits of Coding on Age of Information in Broadcast Networks

Xingran Chen, Shirin Saeedi Bidokhti|arXiv (Cornell University)|Apr 22, 2019

Age of Information Optimization35 references4 citations

TL;DR

This paper studies age of information (AoI) in two-user broadcast networks with feedback, proposing coding-aware scheduling policies that outperform traditional uncoded schemes. It derives a general lower bound on expected weighted sum AoI and shows that coded randomized policies strictly improve AoI over uncoded ones under symmetric dependent erasure channels, with numerical validation for Max-Weight policies.

ABSTRACT

Age of Information (AoI) is studied in two-user broadcast networks with feedback, and lower and upper bounds are derived on the expected weighted sum AoI of the users. In particular, a class of simple coding actions is considered and within this class, randomized and deterministic policies are devised. Explicit conditions are found for symmetric dependent channels under which coded randomized policies strictly outperform the corresponding uncoded policies. Similar behavior is numerically shown for deterministic policies.

Motivation & Objective

• To analyze the impact of network coding on age of information (AoI) in two-user broadcast packet erasure channels (BPECs) with feedback.
• To establish a general lower bound on expected weighted sum AoI (EWSAoI) valid for any coding scheme, not just traditional scheduling.
• To design and evaluate randomized and deterministic Max-Weight scheduling policies that prioritize coding actions (uncoded for user 1, uncoded for user 2, or XOR-coded for both) over user selection.
• To identify conditions under which coded policies strictly outperform uncoded policies in terms of AoI, particularly in symmetric BPECs.
• To provide analytical upper bounds on EWSAoI for both randomized and Max-Weight policies, enabling performance comparison.

Proposed method

• Proposes a discrete-time model for two-user BPECs with feedback, where the source transmits either uncoded packets for one user or XOR-coded packets for both.
• Introduces a class of three coding actions: transmit for user 1 only, for user 2 only, or XOR of both packets for simultaneous delivery.
• Derives a general lower bound on EWSAoI using queueing and stochastic process analysis, valid across all coding schemes.
• Designs a stationary randomized policy with probabilities (μ₁, μ₂, μ₃) for the three actions, and derives a closed-form expression for the resulting EWSAoI.
• Applies Lyapunov drift analysis to Max-Weight (MW) policies, deriving an upper bound on EWSAoI by bounding the one-slot drift and using Cauchy-Schwarz and Jensen’s inequalities.
• Uses the structure of queue states and feedback to model the probability of non-empty queues and incorporate them into performance bounds.

Experimental results

Research questions

• RQ1 Under what conditions does network coding reduce the expected weighted sum AoI compared to uncoded transmission in two-user broadcast networks with feedback?
• RQ2 Can randomized coding policies strictly outperform their uncoded counterparts in symmetric BPECs, and if so, what are the explicit conditions?
• RQ3 How does the Max-Weight scheduling policy perform when adapted to prioritize coding actions rather than users, and what upper bound can be placed on its EWSAoI?
• RQ4 Is the general lower bound on EWSAoI tight, and does it hold for all coding schemes, including those that exploit feedback and coding gains?
• RQ5 What is the trade-off between coding delay (waiting for coding opportunities) and age reduction in coded transmission policies?

Key findings

• For symmetric dependent BPECs, coded randomized policies strictly outperform uncoded randomized policies when the channel error probabilities satisfy specific conditions derived from the closed-form EWSAoI expression.
• The general lower bound on EWSAoI applies to any coding scheme, including those using feedback and network coding, and is tighter than prior bounds restricted to traditional scheduling.
• The upper bound on EWSAoI for Max-Weight policies is derived using Lyapunov drift and stochastic inequalities, showing that coding can reduce age even under delay constraints.
• Numerical results confirm that coded Max-Weight policies achieve lower EWSAoI than uncoded MW policies, demonstrating practical gains from coding.
• The derived upper bound for MW policies depends on the probabilities of non-empty queues and channel error rates, with explicit expressions for Φᵢ and Ψᵢ in terms of transmission probabilities and error parameters.