Systematic Luby Transform Codes and Their Soft Decoding

Abstract

Luby Transform codes (LT) were originally designed for the Binary Erasure Channel (BEC) encountered owing to randomly dropped packets in the statistical multiplexing aided classic wireline-based Internet, where transmitted packets are not affected by the fading or noise of the propagation environment of the wireless Internet. For the sake of transmitting data over the BEC routinely encountered in statistical multiplexing aided wireless Internet-style scenarios, we applied the belief propagation algorithm for decoding LT codes and designed a novel version of LT codes, which we refer to as systematic LT codes. When using soft decoding of the proposed systematic LT code, the decoding process becomes capable of preventing the potentially avalanche-like inter-packet error propagation. For example, the systematic LT(1000,3000) code achieved a BER below 10-5 at E b /N 0 = 3.5dB after six decoding iterations. An even lower E b /N 0 of 2.7dB was required, when using a longer systematic LT(10000,30000) code for transmission over the AWGN channel. In the combined BEC-AWGN channel the BER recorded at the output of the systematic LT(1000,3000) code was about 10-5 at E b /N 0 = 4.5dB, when encounter an erasure probability of P e = 0.1.