# On LDPC Code Based Massive Random-Access Scheme for the Gaussian Multiple Access Channel

## TL;DR

This paper enhances a massive random access scheme for Gaussian MAC by optimizing LDPC codes using generalized PEXIT charts, resulting in improved decoding performance and system efficiency.

## Contribution

It introduces a generalized PEXIT chart method to optimize LDPC codes specifically for Gaussian MAC, improving decoding performance over previous schemes.

## Key findings

- Optimized LDPC codes outperform previous designs in simulations.
- The proposed scheme achieves better decoding thresholds and error rates.
- Simulation results align closely with theoretical bounds.

## Abstract

This paper deals with the problem of massive random access for Gaussian multiple access channel (MAC). We continue to investigate the coding scheme for Gaussian MAC proposed by A. Vem et al in 2017. The proposed scheme consists of four parts: (i) the data transmission is partitioned into time slots; (ii) the data, transmitted in each slot, is split into two parts, the first one set an interleaver of the low-density parity-check (LDPC) type code and is encoded by spreading sequence or codewords that are designed to be decoded by compressed sensing type decoding; (iii) the another part of transmitted data is encoded by LDPC type code and decoded using a joint message passing decoding algorithm designed for the T-user binary input Gaussian MAC; (iv) users repeat their codeword in multiple slots. In this paper we are concentrated on the third part of considered scheme. We generalized the PEXIT charts to optimize the protograph of LDPC code for Gaussian MAC. The simulation results, obtained at the end of the paper, were analyzed and compared with obtained theoretical bounds and thresholds. Obtained simulation results shows that proposed LDPC code constructions have better performance under joint decoding algorithm over Gaussian MAC than LDPC codes considered by A. Vem et al in 2017, that leads to the better performance of overall transmission system.