论文标题
构建$ c^\ star $来自自助代码
Construction $C^\star$ from Self-Dual Codes
论文作者
论文摘要
最近将构建$ c^\ star $作为多级构造C（或福尼代码形式）的概括引入，因此编码级别可能取决于。这两种结构通常都没有产生晶格，因此本文的核心思想是呈现3级晶格结构$ C^\ star $ Scheme，该计划承认有效的最近的邻居解码。为了实现这一目标，我们选择级别1和3的耦合代码，并将第二级代码C2设置为独立的线性二进制自动划分代码，该代码已知线性代码家族之间具有丰富的数学结构。我们的主要结果指出了该结构生成晶格的必要条件。然后，我们介绍了有效的晶格和具有良好填料特性的非晶格星座的示例。
Construction $C^\star$ was recently introduced as a generalization of the multilevel Construction C (or Forney's code-formula), such that the coded levels may be dependent. Both constructions do not produce a lattice in general, hence the central idea of this paper is to present a 3-level lattice Construction $C^\star$ scheme that admits an efficient nearest-neighborhood decoding. In order to achieve this objective, we choose coupled codes for levels 1 and 3, and set the second level code C2 as an independent linear binary self-dual code, which is known to have a rich mathematical structure among families of linear codes. Our main result states a necessary and sufficient condition for this construction to generate a lattice. We then present examples of efficient lattices and also non-lattice constellations with good packing properties.
