LDPC Codes

Python implementation and simulation of Low-Density Parity-Check (LDPC) codes for error correction in digital communications.

Overview

LDPC codes are a class of linear error-correcting codes that achieve near-Shannon-limit performance on a wide range of communication channels. This project provides a complete Python implementation of LDPC encoding, decoding, and simulation -- including applications for image and audio transmission over noisy channels.

Features

• LDPC Code Construction -- Generate parity-check matrix (H) and generator matrix (G) with configurable parameters
• Encoding & Decoding -- Full encoding pipeline with belief propagation (Log-BP) decoding
• BER Simulation -- Bit Error Rate analysis across varying SNR levels
• Image Transmission -- Simulate sending images through noisy channels with LDPC protection
• Audio Transmission -- LDPC-coded audio transmission simulation
• Parallel Decoding -- Numba-accelerated parallel decoding implementation
• Visualization -- Matplotlib-based plots for BER curves and transmission results

Project Structure

LDPC-Codes/
├── ldpc/                              # Core LDPC library
│   ├── __init__.py                    # Package exports
│   ├── code.py                        # LDPC code construction (make_ldpc)
│   ├── encoder.py                     # Encoding functions
│   ├── decoder.py                     # Log-BP decoding (with Numba acceleration)
│   ├── utils.py                       # General utilities
│   ├── utils_img.py                   # Image processing utilities
│   ├── utils_audio.py                 # Audio processing utilities
│   ├── ldpc_images.py                 # Image transmission simulation
│   ├── ldpc_audio.py                  # Audio transmission simulation
│   └── _version.py                    # Version information
├── binary/                            # Binary data files
├── data/                              # Sample data for simulations
├── plot_coding_decoding_simulation.py # BER vs SNR simulation script
├── plot_image_transmission.py         # Image transmission demo
├── plot_parallel_decoding.py          # Parallel decoding benchmark
└── README.md

Getting Started

Prerequisites

• Python 3.8+
• NumPy
• SciPy
• Matplotlib
• Numba (for parallel decoding acceleration)

Installation

git clone https://github.com/Sagargupta16/LDPC-Codes.git
cd LDPC-Codes
pip install numpy scipy matplotlib numba

Usage

Basic Coding & Decoding Simulation

python plot_coding_decoding_simulation.py

This generates a BER vs SNR curve showing error correction performance:

• Creates an LDPC code with n=30 coded bits, d_v=2, d_c=3
• Simulates 50 transmissions per SNR point across SNR range [-2, 10] dB
• Plots the resulting Bit Error Rate curve

Image Transmission

python plot_image_transmission.py

Demonstrates LDPC-coded image transmission through a noisy AWGN channel with visual comparison of original vs. received images.

Parallel Decoding Benchmark

python plot_parallel_decoding.py

Benchmarks Numba-accelerated parallel decoding against standard sequential decoding.

Key Parameters

Parameter	Description	Typical Value
n	Number of coded bits	30-1000+
d_v	Column weight (ones per column in H)	2-4
d_c	Row weight (ones per row in H)	3-6
snr	Signal-to-Noise Ratio (dB)	-2 to 10
maxiter	Maximum decoding iterations	50-100

API Reference

from ldpc import make_ldpc, encode, decode, get_message

# Create LDPC code
H, G = make_ldpc(n, d_v, d_c, seed=seed, systematic=True, sparse=True)

# Encode message
y = encode(G, message, snr, seed=seed)

# Decode received signal
D = decode(H, y, snr, maxiter=50)

# Extract original message
x = get_message(G, D)

License

MIT