We consider reliable and secure communication over intersymbol interference wiretap channels (ISI-WTCs). In particular, we first derive an achievable secure rate for ISI-WTCs without imposing any constraints on the input distribution. Afterwards, we focus on the setup where the input distribution of the ISI-WTC is constrained to be a time-invariant finite-order Markov chain. Optimizing the parameters of this Markov chain toward maximizing the achievable secure rates 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 rate function with a suitable~surrogate function whose maximum can be found efficiently. Although the secure rates achieved in the unconstrained setup are potentially larger than the secure rates achieved in the constrained setup, the latter setup has the advantage of leading to efficient algorithms for estimating and optimizing the achievable secure rates, and also has the benefit of being the basis of efficient coding schemes.
翻译:我们考虑在符号间干扰窃听信道(ISI-WTC)上进行可靠和安全的通信。特别是,我们首先推导了一种可实现的无限制输入分布的ISI-WTC安全速率。随后,我们专注于输入分布受限于时间不变有限阶Markov链的设置。根据这个马尔可夫链的参数最大化可实现的安全速率是一个普遍的计算难题,因此,为了找到局部最优解,我们提出了一种迭代算法,在每次迭代时将安全速率函数替换为适当的代理函数,其最大值可以有效地找到。虽然无约束设置中实现的安全速率潜在更高,但后一种设置具有优化可实现的安全速率的有效算法的优点,并且也具有高效编码方案的基础。