# Lightweight FEC: Rectangular Codes with Minimum Feedback Information

## TL;DR

This paper introduces a lightweight hybrid error correction protocol that minimizes feedback, reduces bandwidth, and efficiently repairs transmission errors over noisy channels, outperforming TCP in iteration reduction.

## Contribution

It presents a novel rectangular error-correcting code combined with backward error correction, with a linear-time algorithm for minimal feedback, and analyzes its asymptotic bandwidth efficiency.

## Key findings

- Reduces number of iterations by up to 40% compared to TCP.
- Achieves asymptotically small backward channel bandwidth use.
- Provides explicit asymptotic expansion for expected feedback bandwidth.

## Abstract

We propose a hybrid protocol combining a rectangular error-correcting code - paired with an error-detecting code - and a backward error correction in order to send packages of information over a noisy channel. We depict a linear-time algorithm the receiver can use to determine the minimum amount of information to be requested from the sender in order to repair all transmission errors. Repairs may possibly occur over several cycles of emissions and requests. We show that the expected bandwidth use on the backward channel by our protocol is asymptotically small. In most configurations we give the explicit asymptotic expansion for said expectation. This is obtained by linking our problem to a well known algorithmic problem on a gadget graph, feedback edge set. The little use of the backward channel makes our protocol suitable where one could otherwise simply use backward error correction, e.g. TCP, but where overly using the backward channel is undesirable. We confront our protocol to numerical analysis versus TCP protocol. In most cases our protocol allows to reduce the number of iterations down to 60%, while requiring only negligibly more packages.