Resource allocation for secret key agreement by LLR thresholding over parallel channels

We consider a channel-model based secret key agreement (SKA) over parallel channels, where Alice transmits a random sequence of bits, and Bob selects those having an absolute value of log-likelihood ratio (LLR) larger than a given threshold. Distillation and reconciliation processes follow, independently on each channel. Assuming a total transmit power constraint, we aim at choosing both the LLR threshold and the transmit power on each channel, in order to maximize the secret key throughput (SKT), under a full channel state information of both legitimate and eavesdropper channels. A two-step solution is considered. First the LLR threshold is determined on a per-channel basis for a given power allocation by numerical methods. Then we fit the SKT as a function of the transmit power by an exponential function and the power allocation problem is solved in closed form. Extensive simulation results show accuracy of the fitting function and the importance of the optimization, also for practical reconciliation processes.