[TCOM] Tight Upper Bounds on the BLER of Spinal codes over the AWGN Channel

This paper establishes an upper bound on the block error rate (BLER) of Spinal codes, the first rateless codes proven to achieve Shannon capacity in additive white Gaussian noise (AWGN) and binary symmetric channels (BSC). Unlike the conventional reliance on the 1965 Gallager random coding bound [1, Theorem 5.6.2] for deriving upper bounds, as illustrated in 2016 [2] by Yu et. al, this study deviates by noting that Gallager’s bound may not adequately represent the distinct properties of specific random codes like Spinal codes and may result in loose bounding performance. We thus introduce novel techniques to refine existing results and enhance the bounding tightness. Our main results are two explicit upper bounds on the BLER of Spinal codes over the AWGN channel, accompanied by theoretical proofs that validate their tightness. Potential applications of the bounds and insights for the coding design are explored in this work.