# Spatially Coupled LDPC Codes and the Multiple Access Channel

## TL;DR

This paper presents a novel application of spatially coupled LDPC codes in a non-orthogonal multiple access scheme, achieving excellent thresholds, flexibility, and low complexity for multi-user communication over various channels.

## Contribution

It introduces a universal SC-LDPC based scheme with outer repetition coding for flexible multi-user access, verified by density evolution and simulations, suitable for Rayleigh channels.

## Key findings

- Achieves near-capacity decoding thresholds for multi-user channels.
- Provides a flexible scheme adaptable to different user loads and rates.
- Demonstrates effective performance on Rayleigh fading channels.

## Abstract

We consider spatially coupled low-density parity-check (SC-LDPC) codes within a non-orthogonal interleave division multiple access (IDMA) scheme to avoid cumbersome degree profile matching of the LDPC code components to the iterative multi-user detector (MUD). Besides excellent decoding thresholds, the approach benefits from the possibility of using rather simple and regular underlying block LDPC codes owing to the universal behavior of the resulting coupled code with respect to the channel front-end, i.e., the iterative MUD. Furthermore, an additional outer repetition code makes the scheme flexible to cope with a varying number of users and user rates, as the SC-LDPC itself can be kept constant for a wide range of different user loads. The decoding thresholds are obtained via density evolution (DE) and verified by bit error rate (BER) simulations. To keep decoding complexity and latency small, we introduce a joint iterative windowed detector/decoder imposing carefully adjusted sub-block interleavers. Finally, we show that the proposed coding scheme also works for Rayleigh channels using the same code with tolerable performance loss compared to the additive white Gaussian noise (AWGN) channel.