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Multiple-phase codes for detection without carrier phase reference

机译:无载波相位参考的多相编码检测

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We consider the construction and analysis of linear block codes for M-ary phase-shift keying that can be decoded without carrier phase synchronization. Under these circumstances, the function that has a significant impact on performance is the noncoherent distance, analogous to the Euclidean distance for the coherent case. The major difficulty in constructing and analyzing such codes lies in the fact that the noncoherent distance is not a true metric. For this reason, prior work mainly relies on numerical approaches to search for good codes and to determine the corresponding minimum noncoherent distance. We first present a theorem that links the noncoherent distance with the Euclidean and Lee (1958) distances. This theorem allows us to construct good codes and determine their minimum noncoherent distances analytically. Based on this theorem, we classify the codes whose duals consist of a cyclic group. These codes are of minimum redundancy. We further investigate codes with the flavor of Hamming and shortened Hamming codes. Many of these new codes provide significantly larger coding gains than previously known codes. Linear codes derived from code-division multiple-access (CDMA) sequences are considered as well. These codes in general provide rather large coding gains. Finally, an algorithm is introduced that can be appended to any suboptimal decoding technique to enhance the performance.
机译:我们考虑了用于M元相移键控的线性分组码的构造和分析,这些编码可以在不进行载波相位同步的情况下进行解码。在这种情况下,对性能有重大影响的函数是非相干距离,类似于相干情况下的欧几里得距离。构造和分析此类代码的主要困难在于,非相干距离不是真实的度量。因此,先前的工作主要依靠数值方法来搜索良好的代码并确定相应的最小非相干距离。我们首先提出一个定理,该定理将非相干距离与欧几里得距离和李距离(1958)距离联系起来。该定理使我们能够构建良好的代码,并通过分析确定其最小非相干距离。基于该定理,我们将对偶由循环组组成的代码分类。这些代码具有最小的冗余度。我们将进一步研究汉明码和缩短汉明码的代码。这些新代码中的许多代码提供的编码增益比以前已知的代码大得多。还考虑了从码分多址(CDMA)序列派生的线性码。这些代码通常提供相当大的编码增益。最后,介绍了一种算法,可以将其附加到任何次优解码技术中以增强性能。

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