# A Unified Ensemble of Concatenated Convolutional Codes

## TL;DR

This paper presents a unified ensemble framework for turbo-like codes, encompassing main classes such as parallel, serial, hybrid, and braided convolutional codes, with derived density evolution equations over the binary erasure channel.

## Contribution

It introduces a unified ensemble model for various turbo-like codes and demonstrates their equivalent representations through parameter selection, along with density evolution analysis.

## Key findings

- Unified ensemble captures all main turbo-like code classes.
- Density evolution thresholds show similar asymptotic behavior to original codes.
- Equivalent ensembles can be derived for each class through parameter tuning.

## Abstract

We introduce a unified ensemble for turbo-like codes (TCs) that contains the four main classes of TCs: parallel concatenated codes, serially concatenated codes, hybrid concatenated codes, and braided convolutional codes. We show that for each of the original classes of TCs, it is possible to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. We also derive the density evolution (DE) equations for this ensemble over the binary erasure channel. The thresholds obtained from the DE indicate that the TC ensembles from the unified ensemble have similar asymptotic behavior to the original TC ensembles.