Error Floor Analysis of LT Codes over the Additive White Gaussian Noise Channel

We investigate the error floor performance of Luby Transform (LT) codes over the additive white Gaussian noise channel. We first derive a lower bound on the bit error rate for an LT code, which we subsequently use to show that the corresponding error floor is predominantly caused by low-degree variable nodes. Based on this observation, we propose a modified encoding scheme for LT codes that provides a lower error floor with no increase in encoding and decoding complexities. The convergence behavior of the proposed scheme is analyzed using extrinsic information transfer charts, and shown to be similar to the original LT code. Numerical examples demonstrate the improvements of the modified LT code as a stand-alone code and as a component code of a Raptor code.