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We consider transmission over a wiretap channel where both the main channeland the wiretapper's channel are Binary Erasure Channels (BEC). We useconvolutional LDPC ensembles based on the coset encoding scheme. Moreprecisely, we consider regular two edge type convolutional LDPC ensembles. Weshow that such a construction achieves the whole rate-equivocation region ofthe BEC wiretap channel.  Convolutional LDPC ensemble were introduced by Felstr\"om and Zigangirov andare known to have excellent thresholds. Recently, Kudekar, Richardson, andUrbanke proved that the phenomenon of "Spatial Coupling" converts MAP thresholdinto BP threshold for transmission over the BEC.  The phenomenon of spatial coupling has been observed to hold for generalbinary memoryless symmetric channels. Hence, we conjecture that ourconstruction is a universal rate-equivocation achieving construction when themain channel and wiretapper's channel are binary memoryless symmetric channels,and the wiretapper's channel is degraded with respect to the main channel.

Rate-Equivocation Optimal Spatially Coupled LDPC Codes for the BEC Wiretap Channel