# On Timely Channel Coding with Hybrid ARQ

## TL;DR

This paper investigates optimizing timely data delivery in a noisy communication system using hybrid ARQ protocols, focusing on minimizing age-of-information through optimal coding, IR lengths, and waiting policies.

## Contribution

It formulates a general AoI minimization problem with hybrid ARQ, derives an optimal threshold-based waiting policy, and discusses code design for binary symmetric channels.

## Key findings

- Optimal threshold-based waiting policy for AoI minimization.
- Stationary deterministic policies are effective for hybrid ARQ.
- Guidelines for codeword and IR length selection in binary symmetric channels.

## Abstract

A status updating communication system is examined, in which a transmitter communicates with a receiver over a noisy channel. The goal is to realize timely delivery of fresh data over time, which is assessed by an age-of-information (AoI) metric. Channel coding is used to combat the channel errors, and feedback is sent to acknowledge updates' reception. In case decoding is unsuccessful, a hybrid ARQ protocol is employed, in which incremental redundancy (IR) bits are transmitted to enhance the decoding ability. This continues for some amount of time in case decoding remains unsuccessful, after which a new (fresh) status update is transmitted instead. In case decoding is successful, the transmitter has the option to idly wait for a certain amount of time before sending a new update. A general problem is formulated that optimizes the codeword and IR lengths for each update, and the waiting times, such that the long term average AoI is minimized. Stationary deterministic policies are investigated, in which the codeword and IR lengths are fixed for each update, and the waiting time is a deterministic function of the AoI. The optimal waiting policy is then derived, and is shown to have a threshold structure, in which the transmitter sends a new update only if the AoI grows above a certain threshold that is a function of the codeword and IR lengths. Choosing the codeword and IR lengths is discussed in the context of binary symmetric channels.