Error Floor of ML-Decoded Spinal Codes in the Finite Blocklength Regime

Spinal codes are a new family of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">capacity-achieving</i> rateless codes that have been shown to achieve better rate performance compared to Raptor codes, Strider codes, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rateless</i> Low-Density Parity-Check (LDPC) codes. This correspondence addresses the performance limitations of Spinal codes in the finite blocklength regime, uncovering an error floor phenomenon at high Signal-to-Noise Ratios (SNRs) under Maximum Likelihood (ML) Decoding. 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 do not affect the SNR threshold, providing insights into the performance target, the operating SNR region, and the code design.