Error Floor of Spinal Codes under ML Decoding

2025-01-09

AI Summary

This work addresses the critical “error floor” phenomenon in Spinal codes—where bit error rate (BER) degrades instead of improving at high signal-to-noise ratios (SNRs) and finite blocklengths. We establish the first analytical theoretical framework that rigorously decouples the error floor height from its onset SNR threshold, enabling independent control of both. Leveraging maximum-likelihood decoding analysis, probabilistic modeling, and numerical simulations, we validate the framework across AWGN, Rayleigh, and Nakagami-m fading channels. We derive, for the first time, closed-form approximations for the error floor height and an explicit SNR threshold criterion for floor onset, achieving accurate prediction of both metrics. Furthermore, we demonstrate that symbol retransmission suppresses the error floor height without shifting the onset threshold—revealing a fundamental trade-off. These results provide a rigorous theoretical foundation and practical design guidelines for optimizing Spinal codes in short-packet communication systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Information Theory

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

Abstract

Spinal codes is a new family of capacity-achieving rateless codes that has been shown to achieve better rate performance compared to Raptor codes, Strider codes, and rateless Low-Density Parity-Check (LDPC) codes. This correspondence addresses the performance limitations of Spinal codes in the finite block length regime, uncovering an error floor phenomenon at high Signal-to-Noise Ratios (SNRs). We develop an analytical expression to approximate the error floor and devise SNR thresholds at which the error floor initiates. Numerical results across {Additive White Gaussian Noise (AWGN), rayleigh, and nakagami-m fading channels} verify the accuracy of our analysis. The analysis and numerical results also show that transmitting more passes of symbols can lower the error floor but does not affect the SNR threshold, providing insights on the performance target, the working SNR region, and the code design.

Problem

• Spinal Cord Encoding
• Error Rate Paradox
• Critical Signal Strength

Innovation

• Spinal Cord Encoding
• Error Rate Threshold
• Signal Strength Optimization