  In this paper, the design of irregular turbo codes for the binary erasure
channel is investigated. An analytic expression of the erasure probability of
punctured recursive systematic convolutional codes is derived. This exact
expression will be used to track the density evolution of turbo codes over the
erasure channel, that will allow for the design of capacity-approaching
irregular turbo codes. Next, we propose a graph-optimal interleaver for
irregular turbo codes. Simulation results for different coding rates is shown
at the end.
