Constrained Secrecy Capacity of Finite-Input Intersymbol Interference Wiretap Channels

We consider reliable and secure communication over intersymbol interference wiretap channels (ISI-WTCs). In particular, we first examine the setup where the source at the input of an ISI-WTC is unconstrained and then, based on a general achievability result for arbitrary wiretap channels, we derive an achievable secure information rate for this ISI-WTC. Afterwards, we examine the setup where the source at the input of an ISI-WTC is constrained to be a finite-state machine source (FSMS) of a certain order and structure. Optimizing the parameters of this FSMS toward maximizing the secure information rate is a computationally intractable problem in general, and so, toward finding a local maximum, we propose an iterative algorithm that at every iteration replaces the secure information rate function by a suitable surrogate function whose maximum can be found efficiently. Although the secure information rates achieved in the unconstrained setup are expected to be larger than the secure information rates achieved in the constrained setup, the latter setup has the advantage of leading to efficient algorithms for estimating achievable secure rates and also has the benefit of being the basis of efficient encoding and decoding schemes.