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.

翻译：特定信道编码的性能评估一直是编码理论中的重要课题，通常涉及界限技术的使用。本文聚焦于新型容量逼近码族——Spinal码，提出一个综合分析框架，用于在有限码长（FBL）体制下紧密界定Spinal码的块错误率（BLER）上界。首先，我们采用Gallager随机编码界的变体来推导衰落信道上Spinal码的BLER上界。随后，本文在不依赖Gallager随机编码界的情况下推导出新的界限，该界限可在较宽信噪比（SNR）范围内达到可证明的紧致性。本文推导的BLER上界具有普适性，便于评估Spinal码在不同类型快衰落信道上的性能。作为案例研究，本文在瑞利、Nakagami-m和莱斯衰落信道上显式推导了Spinal码的BLER上界。基于这些界限，我们从理论上揭示了ML译码Spinal码的尾部传输模式（TTP）在可靠性性能方面仍保持最优性。仿真实验验证了所提界限的紧致性及所得结论的有效性。