论文标题
多层集成交织的代码：一类层次结构本地可回收代码
Multiple-Layer Integrated Interleaved Codes: A Class of Hierarchical Locally Recoverable Codes
论文作者
论文摘要
集成交错的传统定义（II）代码通常假定组件嵌套代码是芦苇 - 固体（RS）或缩短的芦苇 - 固体代码。通过参加一般的代码，我们提出了扩展的综合交织（EII）代码的递归构造成多层，这一问题引起了文献中的II代码的关注。多层方法允许一个分层方案，其中代码的每一层都提供了不同的位置。特别是，我们介绍了新代码的擦除功能，并表明它们由于其层次结构所需的层次和构造所需的小有限字段而非常适合本地可回收（LRC）代码。多层EII代码的属性，例如它们的最小距离和尺寸，以及它们的擦除解码算法，奇偶校验检查矩阵和性能分析，并提供了示例。最后，我们将观察到高层EII代码的奇偶校验检查矩阵的密度较低。
The traditional definition of Integrated Interleaved (II) codes generally assumes that the component nested codes are either Reed-Solomon (RS) or shortened Reed-Solomon codes. By taking general classes of codes, we present a recursive construction of Extended Integrated Interleaved (EII) codes into multiple layers, a problem that brought attention in literature for II codes. The multiple layer approach allows for a hierarchical scheme where each layer of the code provides for a different locality. In particular, we present the erasure-correcting capability of the new codes and we show that they are ideally suited as Locally Recoverable (LRC) codes due to their hierarchical locality and the small finite field required by the construction. Properties of the multiple layer EII codes, like their minimum distance and dimension, as well as their erasure decoding algorithms, parity-check matrices and performance analysis, are provided and illustrated with examples. Finally, we will observe that the parity-check matrices of high layer EII codes have low density.
