# Protograph LDPC Code Design for Asynchronous Random Access

## TL;DR

This paper designs and evaluates protograph LDPC codes tailored for asynchronous random access channels, demonstrating significant performance gains in supporting more users with reliable decoding.

## Contribution

It introduces a surrogate channel model for asynchronous collisions and proposes optimized protograph LDPC codes that outperform standard codes in this setting.

## Key findings

- Optimized codes increase supported traffic by ~17% at 1% packet loss.
- Abstracted physical layer models overestimate performance for short blocks.
- Codes are effective in both abstracted and realistic channel simulations.

## Abstract

This work addresses the physical layer channel code design for an uncoordinated, frame- and slot-asynchronous random access protocol. Starting from the observation that collisions between two users yield very specific interference patterns, we define a surrogate channel model and propose different protograph low-density parity-check code designs. The proposed codes are both tested in a setup where the physical layer is abstracted, as well as on a more realistic channel model, where finite-length physical layer simulations of the entire asynchronous random access scheme, including decoding are carried out. We find that the abstracted physical layer model overestimates the performance when short blocks are considered. Additionally, the optimized codes show gains in supported channel traffic - a measure of the number of terminals that can be concurrently accommodated on the channel - of around 17% at a packet loss rate of 10^{-2} w.r.t. off-the-shelf codes.