Tool for exploring erasure thresholds in noisy binary communication channels: Analyzing trade-offs between erasure and bit-flip errors for improved reliability and capacity

Modern communication systems face unprecedented challenges in reliably transmitting information across channels that introduce uncertainty through both deliberate erasures (complete symbol loss) and inherent bit-flip errors. This thesis develops a comprehensive framework for optimizing erasure threshold policies in noisy binary channels, with particular inclusion of impulsive noise environments and adaptive coding strategies.We establish theoretical foundations connecting Shannon’s information theory to practical coding schemes (Reed-Solomon and BCH codes), demonstrating how threshold-based erasure policies balance the fundamental trade-off between erasure and error probabilities. The key contribution is an interactive web-based visualization platform that makes abstract erasure channel concepts tangible through real-time parameter manipulation, enabling exploration of capacity curves, probability distributions, and coding performance.For impulsive noise channels, characterized by infrequent but large-amplitude disturbances, we introduce and analyze dual-threshold erasure policies that erase both very small and very large magnitude samples. This approach outperforms traditional single threshold methods by avoiding decisions on impulse-dominated samples. Through gradient-based impact analysis, we quantify the marginal contribution of each threshold by measuring capacity degradation when either threshold is removed, revealing that outer threshold importance evolves from negligible (1-2% impact) in low-impulse scenarios to dominant (40-50% impact) in heavy-impulse environments across varying impulsive noise regimes.Beyond theoretical analysis, we demonstrate how the Binary Erasure Channel abstraction provides a precise model for diverse physical phenomena: packet losses in networks (satellite, cellular, IoT), straggler tolerance in distributed computing, decoherence in quantum systems, and fault tolerance in edge computing. Each application domain reveals unique design trade-offs unified by erasure channel theory.The thesis culminates with an analysis of emerging applications in video streaming, distributed machine learning, and classical-quantum hybrid systems. We identify open research questions and propose directions for future work at the intersection of information theory, coding theory, and interactive visualization.By combining rigorous mathematical exposition with an interactive computational platform, this work contributes both to pedagogical understanding and research methodology in erasure channel analysis. The open-source codebase (Rust/WebAssembly backend with Svelte frontend) enables researchers and practitioners to explore, validate, and extend these concepts to new domains.