  A visible light communication broadcast channel is considered, in which a
transmitter luminaire communicates with two legitimate receivers in the
presence of an external eavesdropper. A number of trusted cooperative
half-duplex relay luminaires are deployed to aid with securing the transmitted
data. Transmitters are equipped with single light fixtures, containing multiple
light emitting diodes, and receiving nodes are equipped with single
photo-detectors, rendering the considered setting as a single-input
single-output system. Transmission is amplitude-constrained to maintain
operation within the light emitting diodes' dynamic range. Achievable secrecy
rate regions are derived under such amplitude constraints for this
multi-receiver wiretap channel, first for direct transmission without the
relays, and then for multiple relaying schemes: cooperative jamming,
decode-and-forward, and amplify-and-forward. Superposition coding with uniform
signaling is used at the transmitter and the relays. Further, for each relaying
scheme, secure beamforming vectors are carefully designed at the relay nodes in
order to hurt the eavesdropper and/or benefit the legitimate receivers.
Superiority of the proposed relaying schemes, with secure beamforming, is shown
over direct transmission. It is also shown that the best relaying scheme
depends on how far the eavesdropper is located from the transmitter and the
relays, the number of relays, and their geometric layout.
