# Adaptive Causal Network Coding with Feedback

## TL;DR

This paper introduces an adaptive causal network coding algorithm with feedback that learns channel erasures and optimizes transmission, significantly improving throughput and delay performance in bursty channels for low-latency applications.

## Contribution

The paper presents a novel AC-RLNC algorithm that adaptively adjusts retransmissions based on feedback, achieving near-capacity throughput and reduced delay in non-asymptotic regimes.

## Key findings

- AC-RLNC achieves over 90% of channel capacity.
- AC-RLNC doubles throughput compared to SR-ARQ in bursty channels.
- AC-RLNC triples the delay performance gains over SR-ARQ.

## Abstract

We propose a novel adaptive and causal random linear network coding (AC-RLNC) algorithm with forward error correction (FEC) for a point-to-point communication channel with delayed feedback. AC-RLNC is adaptive to the channel condition, that the algorithm estimates, and is causal, as coding depends on the particular erasure realizations, as reflected in the feedback acknowledgments. Specifically, the proposed model can learn the erasure pattern of the channel via feedback acknowledgments, and adaptively adjust its retransmission rates using a priori and posteriori algorithms. By those adjustments, AC-RLNC achieves the desired delay and throughput, and enables transmission with zero error probability. We upper bound the throughput and the mean and maximum in order delivery delay of AC-RLNC, and prove that for the point to point communication channel in the non-asymptotic regime the proposed code may achieve more than 90% of the channel capacity. To upper bound the throughput we utilize the minimum Bhattacharyya distance for the AC-RLNC code. We validate those results via simulations. We contrast the performance of AC-RLNC with the one of selective repeat (SR)-ARQ, which is causal but not adaptive, and is a posteriori. Via a study on experimentally obtained commercial traces, we demonstrate that a protocol based on AC-RLNC can, vis-`a-vis SR-ARQ, double the throughput gains, and triple the gain in terms of mean in order delivery delay when the channel is bursty. Furthermore, the difference between the maximum and mean in order delivery delay is much smaller than that of SR-ARQ. Closing the delay gap along with boosting the throughput is very promising for enabling ultra-reliable low-latency communications (URLLC) applications.