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

TL;DR

This paper investigates the error floor phenomenon of ML-decoded Spinal codes in finite blocklength regimes, providing analytical expressions, thresholds, and numerical validation across various channels to inform code design and performance expectations.

Contribution

It introduces an analytical model for the error floor of Spinal codes, identifies SNR thresholds for error floor onset, and validates findings through extensive numerical simulations.

Findings

Error floor phenomenon identified at high SNRs.

Transmitting more passes reduces the error floor.

Error floor threshold remains unaffected by additional passes.

Abstract

Spinal codes is a new family of capacity-achieving rateless codes that has been shown to achieve better rate performance compared to Raptor codes, Strider codes, and rateless Low-Density Parity-Check (LDPC) codes. This correspondence addresses the performance limitations of Spinal codes in the finite block length regime, uncovering an error floor phenomenon at high Signal-to-Noise Ratios (SNRs). 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 does not affect the SNR threshold, providing insights on the performance target, the working SNR region, and the code design.