Secrecy capacity of the ergodic layered erasure wiretap channel

We consider the layered erasure wiretap channel which can also be viewed as the time varying version of the deterministic model of the wiretap channel and characterize its secrecy capacity. We assume an arbitrary fading statistics for the erasure probabilities of the layers and assume that only the fading statistics is known at the transmitter while the instantaneous erasure information, i.e., which layers are erased in a particular channel use, is known at both the receivers. The converse is based on an enhancement technique where we first construct an enhanced wiretap channel and then derive upper bound to the secrecy capacity of the enhanced channel. On the achievability side we show that a coding scheme, in which information is transmitted only via a subset of the layers chosen carefully depending on the channel statistics and independent coding is done across different layers in this subset, can achieve the upper bound.