# Time-Invariant LDPC Convolutional Codes

## TL;DR

This paper introduces a simple class of time-invariant LDPC convolutional codes with large constraint lengths that demonstrate threshold saturation and promising performance, making them attractive for practical implementations.

## Contribution

The paper presents a new, highly simple variant of spatially coupled codes that maintains threshold saturation and performance benefits with minimal parameters.

## Key findings

- Codes exhibit threshold saturation behavior.
- Performance comparable to more complex spatially coupled codes.
- Potential for efficient implementation due to simplicity.

## Abstract

Spatially coupled codes have been shown to universally achieve the capacity for a large class of channels. Many variants of such codes have been introduced to date. We discuss a further such variant that is particularly simple and is determined by a very small number of parameters. More precisely, we consider time-invariant low-density convolutional codes with very large constraint lengths. We show via simulations that, despite their extreme simplicity, such codes still show the threshold saturation behavior known from the spatially coupled codes discussed in the literature. Further, we show how the size of the typical minimum stopping set is related to basic parameters of the code. Due to their simplicity and good performance, these codes might be attractive from an implementation perspective.