A new method is explored for analyzing the performance of coset codes over the binary erasure wiretap channel (BEWC) by decomposing the code over subspaces of the code space. This technique leads to an improved algorithm for calculating equivocation loss. It also provides a continuous-valued function for equivocation loss, permitting proofs of local optimality for certain finite-blocklength code constructions, including a code formed by excluding from the generator matrix all columns which lie within a particular subspace. Subspace decomposition is also used to explore the properties of an alternative secrecy code metric, the chi squared divergence. The chi squared divergence is shown to be far simpler to calculate than equivocation loss. Additionally, the codes which are shown to be locally optimal in terms of equivocation are also proved to be globally optimal in terms of chi squared divergence.

翻译：提出了一种通过将陪集码在码空间的子空间上进行分解来分析其在二进制擦除窃听信道（BEWC）上性能的新方法。该技术改进了计算密文等可解性损失的算法，并提供了等可解性损失的连续值函数，从而能够证明某些有限块长码构造的局部最优性，其中包括一种通过从生成矩阵中排除位于特定子空间中的所有列而形成的码。此外，子空间分解还被用于探索替代性保密码度量——卡方散度的性质。结果表明，卡方散度的计算远比等可解性损失简单。同时，在等可解性方面被证明是局部最优的码，在卡方散度方面也被证明是全局最优的。