论文标题
关于通过单个奇偶校验构建的晶格解码
On the decoding of lattices constructed via a single parity check
论文作者
论文摘要
本文调查了一组出色的晶格的解码：我们在统一的框架中处理尺寸24的水ech晶格，尺寸72中的Nebe晶格和Barnes-Wall Lattices。一个新的有趣的晶格被构建为在水ech晶格上的单一奇偶校验原理的简单应用。这些晶格的常见方面是可以通过单个奇偶校验检查或通过K-IN构造获得它们。我们利用这些结构来引入一个新的有效范式进行解码。这导致高斯通道上有效的列表解码器和准最佳解码器。提供了新解码器的理论和实用性（点误差概率和复杂性）。
This paper investigates the decoding of a remarkable set of lattices: We treat in a unified framework the Leech lattice in dimension 24, the Nebe lattice in dimension 72, and the Barnes-Wall lattices. A new interesting lattice is constructed as a simple application of single parity-check principle on the Leech lattice. The common aspect of these lattices is that they can be obtained via a single parity check or via the k-ing construction. We exploit these constructions to introduce a new efficient paradigm for decoding. This leads to efficient list decoders and quasi-optimal decoders on the Gaussian channel. Both theoretical and practical performance (point error probability and complexity) of the new decoders are provided.
