An Optimal Degree Distribution Design and a Conditional Random Integer Generator for the Systematic Luby Transform Coded Wireless Internet

Recently, the authors of this paper proposed systematic Luby transform (SLT) codes and their soft decoding using the classic loglikelihood message passing algorithm for transmission over hostile Wireless Internet channels, where the transmitted data is affected by both packet loss events and random Gaussian noise. This scheme is further improved here with the aid of a new degree distribution and a novel random integer generator, which are termed as the truncated degree distribution and the conditional random integer generator. The SLT code using the new design is capable of achieving BER les 10^-5 at low E_b/N₀ values. For example, the SLT(1200,3600) code attains BER < lCT5 in excess of an Eb/No value of 1.5 dB for transmission over the AWGN channel and above 3.5 dB over the uncorrelated Rayleigh channel if additionally a packet erasure probability Pe of 0.1 is inflicted, an Eb/No value above 2 dB is required for transmission over the AWGN channel and in excess of 4 dB over the uncorrelated Rayleigh channel, when using a maximum of Iter = 20 iterations and quadrature phase- shift keying.