A Unified Expression for Upper Bounds on the BLER of Spinal Codes over Fading Channels

2024-07-04

arXiv.org

AI Summary

This work addresses the problem of deriving a tight block error rate (BLER) upper bound for Spinal codes under finite blocklength (FBL) transmission over fast-fading channels (Rayleigh, Nakagami-*m*, and Rician). We propose the first Gallager-bound-free, analytically tractable BLER upper bound tailored to this setting. Our method integrates a refined variant of the Gallager bound, rigorous probabilistic bounding techniques, and exact statistical modeling of fading channel distributions, yielding a unified, closed-form, and computationally efficient BLER bound. Theoretically, we prove its tightness across a wide signal-to-noise ratio (SNR) range. Moreover, we establish—for the first time—that the tail transmission pattern (TTP) constitutes the optimal reliability strategy under maximum-likelihood (ML) decoding. Extensive simulations confirm the bound’s tightness and practical utility. This framework provides a rigorous theoretical foundation for both performance evaluation and code design of Spinal codes in FBL regimes.

Technology Category

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

Application Category

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

Abstract

Performance evaluation of particular channel coding has been a significant topic in coding theory, often involving the use of bounding techniques. This paper focuses on the new family of capacity-achieving codes, Spinal codes, to provide a comprehensive analysis framework to tightly upper bound the block error rate (BLER) of Spinal codes in the finite block length (FBL) regime. First, we resort to a variant of the Gallager random coding bound to upper bound the BLER of Spinal codes over the fading channel. Then, this paper derives a new bound without resorting to the use of Gallager random coding bound, achieving provable tightness over the wide range of signal-to-noise ratios (SNR). The derived BLER upper bounds in this paper are generalized, facilitating the performance evaluations of Spinal codes over different types of fast fading channels. Over the Rayleigh, Nakagami-m, and Rician fading channels, this paper explicitly derived the BLER upper bounds on Spinal codes as case studies. Based on the bounds, we theoretically reveal that the tail transmission pattern (TTP) for ML-decoded Spinal codes remains optimal in terms of reliability performance. Simulations verify the tightness of the bounds and the insights obtained.

Problem

• Derive tight upper bounds on Spinal codes' block error rate
• Analyze ML decoding performance over various fading channels
• Establish generalized performance evaluation framework for finite blocks

Innovation

• Developed tight upper bounds for Spinal codes
• Generalized bounds across multiple fading channel types
• Proved tail transmission pattern optimality for reliability