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In this paper we investigate the decoding of parallel turbo codes over the binary erasure channel suited for upper-layer error correction. The proposed algorithm performs ldquoon-the-flyrdquo decoding, i.e. it starts decoding as soon as the first symbols are received. This algorithm compares with the iterative decoding of codes defined on graphs , in that it propagates in the trellises of the turbo code by removing transitions in the same way edges are removed in a bipartite graph under message-passing decoding. Performance comparison with LDPC codes for different coding rates is shown.