  In this paper, we study the frequency-selective broadcast channel with
confidential messages (BCC) in which the transmitter sends a confidential
message to receiver 1 and a common message to receivers 1 and 2. In the case of
a block transmission of N symbols followed by a guard interval of L symbols,
the frequency-selective channel can be modeled as a N * (N+L) Toeplitz matrix.
For this special type of multiple-input multiple-output (MIMO) channels, we
propose a practical Vandermonde precoding that consists of projecting the
confidential messages in the null space of the channel seen by receiver 2 while
superposing the common message. For this scheme, we provide the achievable rate
region, i.e. the rate-tuple of the common and confidential messages, and
characterize the optimal covariance inputs for some special cases of interest.
It is proved that the proposed scheme achieves the optimal degree of freedom
(d.o.f) region. More specifically, it enables to send l <= L confidential
messages and N-l common messages simultaneously over a block of N+L symbols.
Interestingly, the proposed scheme can be applied to secured multiuser
scenarios such as the K+1-user frequency-selective BCC with K confidential
messages and the two-user frequency-selective BCC with two confidential
messages. For each scenario, we provide the achievable secrecy degree of
freedom (s.d.o.f.) region of the corresponding frequency-selective BCC and
prove the optimality of the Vandermonde precoding. One of the appealing
features of the proposed scheme is that it does not require any specific
secrecy encoding technique but can be applied on top of any existing powerful
encoding schemes.
