Ring Compute-and-Forward Over Block-Fading Channels
Ring Compute-and-Forward Over Block-Fading Channels
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DOI：
10.1109/tit.2019.2927453
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发表时间：
2018-05
影响因子：
2.5
通讯作者：
Shanxiang Lyu;A. Campello;Cong Ling
中科院分区：
文献类型：
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作者：
Shanxiang Lyu;A. Campello;Cong Ling
在准静态信道中的计算和转发（C&F）协议通常采用基于有理数$\mathbb {Z}$、高斯整数$\mathbb {Z} [i]$或爱森斯坦整数$\mathbb {Z} [\omega ]$的格码，而其扩展到更一般的信道通常假设发送端的信道状态信息（CSIT）。在本文中，我们提出了一种新的方案C&F块衰落信道中没有CSIT，这是被称为环C&F，因为衰落系数量化的代数整数环的规范嵌入。由于所采用的代数格的乘法闭包，中继能够解码格码字的代数整数线性组合。我们分析了其可实现的计算速率，并显示它优于传统的C&F的基础上的$\mathbb {Z}$ -格。通过研究Diophantine近似的代数共轭的效果，我们证明了优化计算速率的自由度（DoF）为${n}/{L}$，其中$n$是块的数目，$L$是用户的数目。
The compute-and-forward (C&F) protocol in quasi-static channels normally employs lattice codes based on the rational integers $\mathbb {Z}$ , the Gaussian integers $\mathbb {Z} [i]$ , or the Eisenstein integers $\mathbb {Z} [\omega ]$ , while its extension to more general channels often assumes channel state information at transmitters (CSIT). In this paper, we propose a novel scheme for C&F in block-fading channels without CSIT, which is referred to as ring C&F because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers. Owing to the multiplicative closure of the algebraic lattices employed, a relay is able to decode an algebraic–integer linear combination of lattice codewords. We analyze its achievable computation rates and show it outperforms conventional C&F based on the $\mathbb {Z}$ -lattices. By investigating the effect of the Diophantine approximation by algebraic conjugates, we prove that the degrees of freedom (DoFs) of the optimized computation rate are ${n}/{L}$ , where $n$ is the number of blocks and $L$ is the number of users.