  This paper presents a polar coding scheme to achieve secrecy in block fading
binary symmetric wiretap channels without the knowledge of instantaneous
channel state information (CSI) at the transmitter. For this model, a coding
scheme that hierarchically utilizes polar codes is presented. In particular, on
polarization of different binary symmetric channels over different fading
blocks, each channel use is modeled as an appropriate binary erasure channel
over fading blocks. Polar codes are constructed for both coding over channel
uses for each fading block and coding over fading blocks for certain channel
uses. In order to guarantee security, random bits are introduced at appropriate
places to exhaust the observations of the eavesdropper. It is shown that this
coding scheme, without instantaneous CSI at the transmitter, is secrecy
capacity achieving for the simultaneous fading scenario. For the independent
fading case, the capacity is achieved when the fading realizations for the
eavesdropper channel is always degraded with respect to the receiver. For the
remaining cases, the gap is analyzed by comparing lower and upper bounds.
Remarkably, for the scenarios where the secrecy capacity is achieved, the
results imply that instantaneous CSI does not increase the secrecy capacity.
