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In this paper we prove threshold saturation for spatially coupled turbo codes(SC-TCs) and braided convolutional codes (BCCs) over the binary erasurechannel. We introduce a compact graph representation for the ensembles of SC-TCand BCC codes which simplifies their description and the analysis of themessage passing decoding. We demonstrate that by few assumptions in theensembles of these codes, it is possible to rewrite their vector recursions ina form which places these ensembles under the category of scalar admissiblesystems. This allows us to define potential functions and prove thresholdsaturation using the proof technique introduced by Yedla et al..

Threshold Saturation for Spatially Coupled Turbo-like Codes over the Binary Erasure Channel