The APLOE research project combines two exciting ideas, that of using the signal properties at the physical layer to secure a communication and that of transmitting at a rate higher than the Nyquist. In respect to the first aspect, the idea of using a helping interferer is employed with a few modifications. Shannon proved that the maximum entropy for the received signals is achieved (and as a result the channel capacity is maximum) when the possible received signals form a white noise ensemble. Reversing the argument, this project proposes to decrease the wiretapper channel capacity (increasing therefore the system secrecy capacity) by designing the transmitted signal so that the wiretapper receives signals that belong to a coloured signal ensemble. The legitimate receiver on the other hand can rely on a-priori knowledge of a symmetric secret key to suppress part of the received signal, so that the demodulator receives signals from a white noise ensemble and the main channel capacity is not compromised.
In order to generate suitably correlated signals we make use of a theoretical result of fundamental importance in communication theory; that a class of functions occupying a bandwidth of approximately B Hz and of duration of approximately T secs has about 2BT degrees of freedom, i.e. it can be specified by approximately 2BT numbers. Our motivation is to generate MOFDM signals that are practically undetectable to all, but the legitimate receiver holding the key. Towards this end, we propose the employment of faster than Nyquist FDM signals with a number of carriers, so that the amount of transmitted data exceeds the channel degrees of freedom. Considered from an information theoretic point of view, the aspiration is that the signals intercepted by the eavesdropper in Additive White Gaussian Noise (AWGN) channels belong to a coloured signal ensemble. Therefore, the wiretapper channel capacity decreases. Examined from a communication theory point of view, such signals have a large number of vanishing eigenvalues. As a result, the transformation matrix of the wiretapper system linear statistical model becomes severely ill-conditioned, rendering signal detection an ill-posed problem.