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Leech Constellations of Construction-A Lattices

机译：构造星座的水-星座

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The problem of communicating over the additive white Gaussian noise (AWGN) channel with lattice codes is addressed in this paper. Theoretically, Voronoi constellations have proved to yield very powerful lattice codes when the fine/coding lattice is AWGN-good and the coarse/shaping lattice has an optimal shaping gain. However, achieving Shannon capacity with these premises and practically implementable encoding algorithms is in general not an easy task. In this paper, a new way to encode and demap Construction-A Voronoi lattice codes is presented. As a meaningful application of this scheme, the second part of the paper is focused on Leech constellations of lowdensity Construction-A (LDA) lattices: LDA Voronoi lattice codes are presented whose numerically measured waterfall region is situated at less than 0.8 dB from Shannon capacity. These LDA lattice codes are based on dual-diagonal nonbinary low-density parity-check codes. With this choice, encoding, iterative decoding, and demapping have all linear complexity in the block length.
机译：本文解决了使用格码在加性高斯白噪声（AWGN）通道上进行通信的问题。从理论上讲，当精细/编码晶格为AWGN良好且粗糙/成形晶格具有最佳整形增益时，Voronoi星座已证明会产生非常强大的晶格码。然而，利用这些前提和实际可行的编码算法来实现香农容量通常不是一件容易的事。本文提出了一种编码和解映射Construction-A Voronoi格码的新方法。作为该方案的有意义的应用，本文的第二部分着重于低密度结构A（LDA）晶格的水ch星座：提出了LDA Voronoi晶格代码，其数值测量的瀑布区域位于距Shannon容量不到0.8 dB的位置。这些LDA格码基于双对角非二进制低密度奇偶校验码。通过这种选择，编码，迭代解码和解映射在块长度上都具有线性复杂度。

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