📡 Digital Communications & Error Correction

👤 Author

Vincent Bevia – POS Architect @ MultiSafepay | Former Telecom Engineer @ COMTECH (EFData) & Fairchild | Cryptography & Signal Processing Enthusiast

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🧭 Overview

This project explores the fundamental principles and practical techniques of digital communication systems, focusing on modulation, channel models, and error correction coding using Python simulations and visualizations.

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📁 Contents

1. 🧮 Modulation Techniques • Binary Phase Shift Keying (BPSK) • Quadrature Amplitude Modulation (QAM – 4-QAM, 16-QAM) • Gray-coded Mapping • Constellation Diagrams • Signal with AWGN + Phase Noise

2. 📡 Channel Models • Additive White Gaussian Noise (AWGN) • Phase noise modeling • Timing jitter (TBD) • Fading channels (optional future section)

3. 🧬 Error Correction Coding

🔸 Convolutional Codes • Encoding logic • Trellis diagrams • Viterbi algorithm • Bit Error Rate (BER) simulation with/without noise

🔸 Block Codes • Reed-Solomon codes (RS) • Hamming codes • Error detection & correction limits • BER performance with noisy channels

🔸 Advanced Coding (optional/future) • LDPC codes • Turbo codes • Polar codes

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🧪 Simulations

Each notebook or module includes:

✅ Bit generation ✅ Modulation (e.g., 16-QAM) ✅ Noise injection (AWGN, phase noise) ✅ Demodulation ✅ Error correction (Viterbi, RS) ✅ Bit Error Rate (BER) analysis

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🔧 Requirements • Python 3.10+ • numpy, matplotlib, scipy, reedsolo, etc.

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🚀 Getting Started

Clone the repo and run:

python qam_with_viterbi_sim.py

Or explore each section via Jupyter notebooks.

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📚 References • “Digital Communications” by John G. Proakis • “Error Control Coding” by Lin & Costello • ITU & DVB Standards for channel coding

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🛠 Future Work • Add soft-decision decoding • Simulate fading and inter-symbol interference • Build a GUI to visualize signal flow in real-time

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