# Density Evolution Analysis of Partially Information Coupled Turbo Codes on the Erasure Channel

## TL;DR

This paper analyzes the performance of partially information coupled turbo codes on the erasure channel, deriving exact density evolution equations to predict decoding thresholds and demonstrating improved error performance over uncoupled codes.

## Contribution

It provides the first detailed density evolution analysis for PIC-TCs, enabling precise threshold computation and performance comparison with uncoupled turbo codes.

## Key findings

- Derived exact density evolution equations for PIC-TCs
- Predicted belief propagation decoding thresholds accurately
- Showed improved error performance over uncoupled turbo codes

## Abstract

In this paper, we investigate the performance of a class of spatially coupled codes, namely partially information coupled turbo codes (PIC-TCs) over the binary erasure channel (BEC). This class of codes enjoy flexible code rate adjustment by varying the coupling ratio. Moreover, the coupling method can be directly applied to any component codes without changing the encoding and decoding architectures of the underlying component codes. However, the theoretical performance of PIC-TCs has not been fully investigated. For this work, we consider the codes that have coupling memory $m$ and study the corresponding graph model. We then derive the exact density evolution equations for these code ensembles with any given coupling ratio and coupling memory $m$ to precisely compute their belief propagation decoding thresholds for the BEC. Our simulation results verify the correctness of our theoretical analysis and also show better error performance over uncoupled turbo codes with a variety of code rates on the BEC.