Variable-Length Stop-Feedback Coding for Minimum Age of Incorrect Information

TL;DR

The paper studies minimizing AoII for a Markov source monitored through a Gaussian channel using variable-length stop-feedback (VLSF) codes with non-instantaneous feedback. It formulates AoII optimization and delay optimization as infinite-horizon MDPs with states capturing transmission progress and feedback timing, solved via Relative Value Iteration, and uses non-asymptotic decoding bounds to approximate packet-level success probabilities. Key findings show that AoII-optimal and delay-optimal feedback sequences can differ, and that periodic feedback schemes often perform nearly as well as AoII-optimal ones, providing a robust, implementable guideline for feedback scheduling in finite-blocklength regimes. These results illuminate the trade-offs between delay and information freshness and offer practical directions for designing feedback strategies in low-latency remote monitoring systems.

Abstract

The Age of Incorrect Information (AoII) is studied within the context of remote monitoring a Markov source using variable-length stop-feedback (VLSF) coding. Leveraging recent results on the non-asymptotic channel coding rate, we consider sources with small cardinality, where feedback is non-instantaneous as the transmitted information and feedback message have comparable lengths. We focus on the feedback sequence, i.e. the times of feedback transmissions, and derive AoII-optimal and delay-optimal feedback sequences. Our results showcase the impact of the feedback sequence on the AoII, revealing that a lower average delay does not necessarily correspond to a lower average AoII. We discuss the implications of our findings and suggest directions for coding scheme design.

Figures (8)

• Figure 1: An example where a binary source is sampled and transmitted at every time slot. Successful decodings occur at time slots $d_i$, $i=1,2,3$, whereas the respective samples were generated at slots $s_i=d_i-1$. The error describes the mismatch between the source and the received values at the monitor. The AoII measures the time the error has been positive.
• Figure 2: The symmetric Markov data source under consideration.
• Figure 3: The AoII process in the absence of successful decodings.
• Figure 4: Average AoII as a function of SNR for feedback delay $\beta=1$ and $k=10$ bits.
• Figure 6: Average delay as a function of SNR for feedback delay $\beta=1$ and $k=10$ bits.

Theorems & Definitions (5)

• Remark 1
• Remark 2
• Definition 1: AoII-optimal Feedback Sequence MDP
• Definition 2: Delay-optimal Feedback Sequence MDP
• Definition 3: Minimum-delay Periodic Feedback Sequence