Lattice constellations and codes from quadratic number fields
Lattice constellations and codes from quadratic number fields
复制标题
来自二次数域的格子星座和代码
DOI：
10.1109/18.923731
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
R. P. Júnior
中科院分区：
文献类型：
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作者：
T. P. D. N. Neto;J. Interlando;Osvaldo Milaré Favareto;M. Elia;R. P. Júnior
在有理数域Q的二次扩展的整数环上，提出了一类新的线性码。本文考虑了二维网格上Mannheim度量的码，特别是对高斯整数和爱森斯坦-雅可比整数上的码进行了广泛的研究。针对任意曼海姆权值误差对传输码向量的两个以上坐标的影响，提出了解码算法。此外，我们还证明了所提出的码在汉明距离方面是最大距离可分离的（MDS）。这种曼海姆度量码的实际意义在于它们在基于正交调幅（QAM）型星座的编码调制方案中的应用，对于这种星座，无论是汉明度量还是李度量都不合适。
We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric module a two-dimensional (2-D) grid, in particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.