Signal sets matched to groups

Loeliger H.-A.

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Signal sets matched to groups

机译：信号组匹配组

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Recently, linear codes over Z/sub M/ (the ring of integers mod M) have been presented that are matched to M-ary phase modulation. The general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes. A definition is given for the notion of matching. It is shown that any signal set in N-dimensional Euclidean space that is matched to an abstract group is essentially what D. Slepian (1968) called a group code for the Gaussian channel. If the group is commutative, this further implies that any such signal set is equivalent to coded phase modulation with linear codes over Z/sub M/. Some further results on such signal sets are presented, and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed.

机译：近来，已经提出了在Z / sub M /上的线性代码（整数环mod M），其与M进制相位调制相匹配。基于这些代码，解决了将信号集匹配到广义线性代数代码的一般问题。给出了匹配概念的定义。结果表明，在N维欧几里得空间中与抽象群匹配的任何信号本质上都是D. Slepian（1968）所说的高斯信道的群码。如果该组是可交换的，则这进一步意味着任何这样的信号集都等效于Z / sub M /上具有线性代码的编码相位调制。给出了关于此类信号集的一些其他结果，并讨论了与非交换组匹配的信号组以及此类组上的线性代码。

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《IEEE Transactions on Information Theory》 |1991年第6期|P.1675-1682|共8页
作者
Loeliger H.-A.;
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正文语种 eng
中图分类无线电电子学、电信技术;
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机译：在几何均匀信号集和与组匹配的信号集
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3. On the construction and labelling of geometrically uniform signal sets in ?2 matched to additive quotient groups [J] . Edson Donizete de Carvalho, Reginaldo Palazzo Jr., Marcelo Firer Journal of Applied Mathematics and Computing . 2008,第1a2期

机译：与加性商群匹配的？2 中几何均匀信号集的构造和标记
4. On Geometrically Uniform Signal Sets and Signal Sets Matched to Groups [C] . Zhe-xian Wan . 2001

机译：关于几何均匀信号集和与组匹配的信号集
5. Optimizing MIMO equalization of QAM signals based on constant modulus algorithm and alphabet matched algorithm. [D] . Taiwo, Peter O. 2015

机译：基于恒模算法和字母匹配算法优化QAM信号的MIMO均衡。
6. Constraining PERMANOVA and LDM to within-set comparisons by projection improves the efficiency of analyses of matched sets of microbiome data [O] . Zhengyi Zhu, Glen A. Satten, Caroline Mitchell, 2021

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7. Figure 7: GSEA enrichment plots showed that eleven gene sets related to tumor signaling pathways (adherens junction (A), calcium signaling pathway (B), cytokine-cytokine receptor interaction (C), ECM receptor interaction (D), hedgehog signaling pathway (E), JAK–STAT signaling pathway (F), MAPK signaling pathway (G), TGF beta signaling pathway (H), Toll–like receptor signaling pathway (I), VEGF signaling pathway (J), Wnt signaling pathway (K)) were enriched in the high SNAP25 expression group. [O] . -1

机译：图7：GSEA富集图显示了与肿瘤信号传导途径有关的11基因集（粘附结（A），钙信号通路（B），细胞因子 - 细胞因子受体相互作用（C），ECM受体相互作用（D），Hedgehog信号通路（ e），JAK-STAT信令途径（F），MAPK信号通路（G），TGFβ信号通路（H），TOL样受体信号传导途径（I），VEGF信号通路（J），WNT信号通路（K））富集在高Snap25表达组中。
8. Tacan Test Signal Set and Dme Test Signal Set. Phase I [R] . Mimken, F., Hazners, V. 1966

机译：Tacan测试信号集和Dme测试信号集。第一阶段

Signal sets matched to groups

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