Study of Second-Order Memory Based LT Encoders

Abstract

LT encoder design has always been a basic and crucial topic ever since the development of fountain codes. The memory based LT encoders (MBLTEs) aim at further improving the code performance by managing the input symbols’ degree distribution after an output symbols’ degree distribution is determined. Previous work has shown that the MBLTE has a faster decoder convergence and a lower bit error rate (BER) than the regular LT encoder with the belief propagation (BP) decoder over binary erasure channels (BECs). However, the study of MBLTEs is limited to first-order MBLTEs, higher-order MBLTEs have not been investigated yet. Therefore, in this paper we study the second-order MBLTE, and propose an algorithm for its realization. Simulation results show that our encoder outperforms the first-order MBLTE in terms of the BER. Our proposed second-order MBLTE performs better either with a short code or with a high erasure probability.