Multi-level LDPC Complete Encoding and Decoding Program

This is a complete encoding and decoding program specifically designed for multi-level LDPC (Low-Density Parity-Check) codes. LDPC codes are channel coding techniques used in communication systems that reduce transmission error rates by introducing carefully designed redundancy. The implementation supports multiple numeral systems such as binary, decimal, and other base representations through configurable parity-check matrix generation and message-passing algorithms. The program features adaptive parameter tuning capabilities for different communication scenarios, allowing optimization of performance metrics like bit error rate (BER) and decoding convergence speed. Key algorithmic components include belief propagation decoding with polynomial-time complexity, soft-decision processing for reliability information, and dynamic check node updating mechanisms. The codebase employs efficient sparse matrix operations for parity-check validation and implements both encoding (generator matrix application) and decoding (iterative message passing) routines. For users working with communication transmission systems, this program serves as a valuable tool that provides flexible configuration options, performance monitoring through convergence tracking, and support for various code rates and block lengths. The implementation includes comprehensive error handling and validation checks to ensure robust operation across different signal-to-noise ratio conditions.