陪集码的子空间分解
Subspace Decomposition of Coset Codes
AI总结：
本文提出基于子空间分解的新方法分析陪集码在二进制擦除窃听信道上的性能，改进了混淆损失计算算法并证明特定有限块长码的局部最优性，同时揭示了卡方散度作为替代度量更易计算且使这些码达到全局最优。
摘要：
本文探索了一种新方法，通过将码分解到码空间的子空间上，来分析陪集码在二进制擦除窃听信道（BEWC）上的性能。该技术改进了计算混淆损失的算法，并提供了混淆损失的连续值函数，从而允许对某些有限块长码构造证明局部最优性，包括一种通过从生成矩阵中排除位于特定子空间内的所有列而形成的码。子空间分解还被用于探索另一种保密码度量——卡方散度的性质。结果表明，卡方散度的计算远比混淆损失简单。此外，在混淆损失方面被证明是局部最优的码，也被证明在卡方散度方面是全局最优的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
