  A secret-key generation scheme based on a layered broadcasting strategy is
introduced for slow-fading channels. In the model considered, Alice wants to
share a key with Bob while keeping the key secret from Eve, who is a passive
eavesdropper. Both Alice-Bob and Alice-Eve channels are assumed to undergo slow
fading, and perfect channel state information (CSI) is assumed to be known only
at the receivers during the transmission. In each fading slot, Alice broadcasts
a continuum of coded layers and, hence, allows Bob to decode at the rate
corresponding to the fading state (unknown to Alice). The index of a reliably
decoded layer is sent back from Bob to Alice via a public and error-free
channel and used to generate a common secret key. In this paper, the achievable
secrecy key rate is first derived for a given power distribution over coded
layers. The optimal power distribution is then characterized. It is shown that
layered broadcast coding can increase the secrecy key rate significantly
compared to single-level coding.
