In this paper we prove threshold saturation for spatially coupled turbo codes
(SC-TCs) and braided convolutional codes (BCCs) over the binary erasure
channel. We introduce a compact graph representation for the ensembles of SC-TC
and BCC codes which simplifies their description and the analysis of the
message passing decoding. We demonstrate that by few assumptions in the
ensembles of these codes, it is possible to rewrite their vector recursions in
a form which places these ensembles under the category of scalar admissible
systems. This allows us to define potential functions and prove threshold
saturation using the proof technique introduced by Yedla et al..Comment: 5 pages, 3figure
