Rate-Distortion-Based Physical Layer Secrecy with Applications to Multimode Fiber

Optical networks are vulnerable to physical layer attacks; wiretappers can improperly receive messages intended for legitimate recipients. Multimode fiber (MMF) transmission can be modeled via a broadcast channel in which both the legitimate receiver's and wiretapper's channels are multiple-input-multiple-output complex Gaussian channels. This work considers the theoretical aspects of this security problem in the domain of a broadcast channel. Source-channel coding analyses based on the use of distortion as the metric for secrecy are developed. Alice has a source sequence to be encoded and transmitted over this broadcast channel so that the legitimate user Bob can reliably decode it while forcing the distortion of the wiretapper, or eavesdropper, Eve's estimate to be as high as possible. Tradeoffs between transmission rate and distortion under two extreme scenarios are examined: the best case where Eve has only her channel output and the worst case where she also knows the past realization of the source. It is shown that under the best case, an operationally separate source-channel coding scheme guarantees maximum distortion at the same rate as needed for reliable transmission. Theoretical bounds are given, and particularized for MMF. Numerical results showing the rate distortion tradeoff are presented and compared with corresponding results for the perfect secrecy case.