Resource allocation for secret transmissions on parallel Rayleigh channels

A transmission between two agents, Alice and Bob, over a set of parallel sub-channels is overheard by a third agent Eve, through a second set of parallel sub-channels. All subchannels are flat with random and independent gains and additive white Gaussian noise (AWGN). Alice splits the total amount of available power among the sub-channels, with the purpose of maximizing the communication rate to Bob, under reliability and secrecy constraints. To this end, two schemes are considered. In one case the secret message is encoded with a single wiretap code and then split among the sub-channels. In the latter case the secret message is first split into a number of sub-messages, each separately encoded and transmitted on a different sub-channel. The achievable secrecy rates under a constraint on the secrecy outage probability (SOP) are derived and closed form expressions for Rayleigh fading sub-channels are obtained. In order to limit the complexity of resources optimization (power and rates) we also consider suboptimal solutions based on the selection of active sub-channels over which power is split either equally or according to a waterfilling algorithm with respect to the Alice-Bob channel.