# Design of Capacity Approaching Ensembles of LDPC Codes for Correlated Sources using EXIT Charts

## TL;DR

This paper develops modified EXIT chart techniques to design LDPC code ensembles that approach capacity for correlated sources, enabling efficient joint decoding with minimal gap to capacity.

## Contribution

It introduces a new EXIT chart analysis tailored for systematic LDPC codes in correlated source scenarios and uses it to design ensembles with near-capacity performance.

## Key findings

- Designed ensembles achieve about 0.2dB gap to capacity at average degree 9.
- Modified EXIT charts effectively analyze systematic LDPC codes for correlated sources.
- Finite length simulations confirm asymptotic performance predictions.

## Abstract

This paper is concerned with the design of capacity approaching ensembles of Low-Densiy Parity-Check (LDPC) codes for correlated sources. We consider correlated binary sources where the data is encoded independently at each source through a systematic LDPC encoder and sent over two independent channels. At the receiver, a iterative joint decoder consisting of two component LDPC decoders is considered where the encoded bits at the output of each component decoder are used at the other decoder as the a priori information. We first provide asymptotic performance analysis using the concept of extrinsic information transfer (EXIT) charts. Compared to the conventional EXIT charts devised to analyze LDPC codes for point to point communication, the proposed EXIT charts have been completely modified to able to accommodate the systematic nature of the codes as well as the iterative behavior between the two component decoders. Then the developed modified EXIT charts are deployed to design ensembles for different levels of correlation. Our results show that as the average degree of the designed ensembles grow, the thresholds corresponding to the designed ensembles approach the capacity. In particular, for ensembles with average degree of around 9, the gap to capacity is reduced to about 0.2dB. Finite block length performance evaluation is also provided for the designed ensembles to verify the asymptotic results.