  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.
