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In this paper, we study systematic Luby Transform (SLT) codes over additivewhite Gaussian noise (AWGN) channel. We introduce the encoding scheme of SLTcodes and give the bipartite graph for iterative belief propagation (BP)decoding algorithm. Similar to low-density parity-check codes, Gaussianapproximation (GA) is applied to yield asymptotic performance of SLT codes.Recent work about SLT codes has been focused on providing better encoding anddecoding algorithms and design of degree distributions. In our work, we proposea novel linear programming method to optimize the degree distribution.Simulation results show that the proposed distributions can provide betterbit-error-ratio (BER) performance. Moreover, we analyze the lower bound of SLTcodes and offer closed form expressions.

Optimization Design and Analysis of Systematic LT codes over AWGN Channel