New Four-Dimensional Signal Constellations From Lipschitz Integers for Transmission Over the Gaussian Channel
New Four-Dimensional Signal Constellations From Lipschitz Integers for Transmission Over the Gaussian Channel
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来自 Lipschitz 整数的新四维信号星座用于通过高斯信道传输
DOI：
10.1109/tcomm.2015.2441691
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发表时间：
2015
影响因子：
8.3
通讯作者：
S. Shavgulidze
中科院分区：
文献类型：
--
作者：
J. Freudenberger;S. Shavgulidze
李普希茨整数商环上的码近年来引起了人们的关注。本文研究了利普希茨整数星座在AWGN信道上的传输性能。提出了一种构造利普希茨整数集的方法，该方法可以得到比普通利普希茨整数星座更好的优点图。特别地，证明了集合划分的概念可以应用于元素个数不是素数的Lipschitz整数商环。证明了将这样的商环划分为可加的子群总是可能的，且每个子群的最小欧氏距离严格大于原集合。所得信号星座在加性高斯白噪声信道上的传输性能优于高斯整数星座和普通利普希茨整数星座。此外，我们还提出了新的信号星座的多级编码结构。
Codes over quotient rings of Lipschitz integers have recently attracted some attention. This work investigates the performance of Lipschitz integer constellations for transmission over the AWGN channel by means of the constellation figure of merit. A construction of sets of Lipschitz integers that leads to a better constellation figure of merit compared to ordinary Lipschitz integer constellations is presented. In particular, it is demonstrated that the concept of set partitioning can be applied to quotient rings of Lipschitz integers where the number of elements is not a prime number. It is shown that it is always possible to partition such quotient rings into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is strictly larger than in the original set. The resulting signal constellations have a better performance for transmission over an additive white Gaussian noise channel compared to Gaussian integer constellations and to ordinary Lipschitz integer constellations. In addition, we present multilevel code constructions for the new signal constellations.