BCH Transmission Simulation

A Python simulation framework for analyzing BCH (Bose-Chaudhuri-Hocquenghem) error-correcting codes performance across various noise conditions, with comprehensive visualization tools for success rates and effective code rates.

Quick Start

Prerequisites

• Python 3.8+ installed on your system
• Git (to clone the repository)

Setup & Installation

1. Clone and navigate to the project

   git clone <repository-url>
   cd BCH_transcoder

2. Create and activate virtual environment

   Windows (PowerShell/CMD):

   python -m venv venv
   .\venv\Scripts\activate

   macOS/Linux:

   python -m venv venv
   source venv/bin/activate

3. Install dependencies

   python -m pip install --upgrade pip
   pip install -r requirements.txt

Usage

1. Try individual BCH codes (interactive demo):

   python bch7_4.py

2. Run full simulation (generates CSV data):

   python transmission_simulation.py

   Note: This may take several minutes to complete

3. Generate plots (creates PNG visualizations):

   python plot_results.py

Results and Visualizations

After running the simulation, the following plots are automatically generated:

Success Rate vs Bit Error Rate (BER)

This plot shows how different BCH codes perform as the bit error rate increases. Higher success rates indicate better error correction capability.

Effective Code Rate vs BER

The effective code rate represents actual data throughput, accounting for both the code rate (k/n) and the success rate at each BER level.

BCH(15,x) Code Family Comparison

These plots focus on the BCH(15,x) family, comparing codes with different error correction capabilities.

Key Insights

• BCH(127,8): Highest error correction (t=31) but very low code rate
• BCH(15,11): Highest information rate but minimal error correction (t=1)
• BCH(15,5): Good balance for moderate error rates with t=3 correction
• All BCH codes significantly outperform unencoded transmission in noisy environments

Available BCH Codes

Code	Parameters	Error Correction Capability	Code Rate
BCH(7,4)	n=7, k=4, t=1	1 bit	4/7 ~~ 0.57
BCH(15,11)	n=15, k=11, t=1	1 bit	11/15 ~~ 0.73
BCH(15,7)	n=15, k=7, t=2	2 bits	7/15 ~~ 0.47
BCH(15,5)	n=15, k=5, t=3	3 bits	5/15 ~~ 0.33
BCH(31,6)	n=31, k=6, t=7	7 bits	6/31 ~~ 0.19
BCH(127,8)	n=127, k=8, t=31	31 bits	8/127 ~~ 0.06

Troubleshooting

Simulation takes too long:

• Edit transmission_simulation.py and reduce SAMPLE_SIZE from 250 to 50-100
• Increase BER_STEP from 0.05 to 0.1 for fewer data points

Testing

Run the test suite to verify everything works correctly:

python -m pytest tests/ -v

Dependencies

• galois: Galois field arithmetic for BCH operations
• matplotlib: Plot generation
• numpy: Numerical computations
• PyInputPlus: Interactive input validation