We consider lattice coding for the Gaussian wiretap channel, where the challenge is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called the secrecy function of a lattice coding scheme was proposed as a design criterion to characterize the eavesdropper's probability of correct decision. In this paper, the family of formally unimodular lattices is presented and shown to possess the same secrecy function behavior as unimodular and isodual lattices. Based on Construction A, we provide a universal approach to determine the secrecy gain, i.e., the maximum value of the secrecy function, for formally unimodular lattices obtained from formally self-dual codes. Furthermore, we show that formally unimodular lattices can achieve higher secrecy gain than the best-known unimodular lattices from the literature.

翻译：我们考虑高斯窃听频道的解密编码,这里的挑战是确保两个被授权方之间的可靠通信,同时防止窃听者学习发送的信息。最近,一项称为拉特斯窃听者编码计划保密功能的措施被提议为设计标准,以描述窃听者正确决定的可能性。在本文中,正式的单式窃听器家族被展示并显示拥有与单式和异式窃听器相同的保密功能。在建筑A中,我们提供了一种通用的方法来确定保密收益,即保密功能的最大值,对于正式的自体代码中获取的正式单式窃听器。此外,我们表明,正式的单式窃听器可以比文献中最知名的单式窃听器获得更高的保密收益。