This paper proposes an expansion graph construction method for medium and short length LT codes. This method expands the Tanner graph with the output node as the root. When the stopping criterion is met, the input node that is not covered or in the deepest expansion layer is randomly selected and connected to the root. The expansion graph method randomly selects input nodes in the largest possible range on the basis of controlling short loops by setting two parameters: the expansion depth threshold and the maximum expandable depth. Simulation results show that this method can effectively improve the performance of medium and short length LT codes compared with random graph and other methods.
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