Recent theoretical developments in coset coding theory have provided continuous-valued functions which give the equivocation and maximum likelihood (ML) decoding probability of coset secrecy codes. In this work, we develop a method for incorporating these functions, along with a complex set of constraints, into a gradient descent optimization algorithm. This algorithm employs a movement cost function and trigonometric update step to ensure that the continuous-valued code definition vector ultimately reaches a value which yields a realizable coset code. This algorithm is used to produce coset codes with blocklength up to a few thousand. These codes were compared against published codes, including both short-blocklength and capacity-achieving constructions. For most code sizes, codes generated using gradient descent outperformed all others, especially capacity-achieving constructions, which performed significantly worse than randomly-generated codes at short blocklength.

翻译：最近，陪集编码理论的理论进展提供了连续值函数，这些函数给出了陪集保密码的疑义度和最大似然（ML）译码概率。在这项工作中，我们开发了一种方法，将这些函数以及一组复杂的约束条件整合到梯度下降优化算法中。该算法采用移动成本函数和三角更新步骤，以确保连续值的码定义向量最终达到能够产生可实现的陪集码的值。该算法用于生成长度达数千的陪集码。这些码与已发表的码进行了比较，包括短码长和达到容量的构造。对于大多数码长，使用梯度下降生成的码优于所有其他码，尤其是达到容量的构造，其在短码长下的性能显著差于随机生成的码。