On the Voronoi Neighbor Ratio for Binary Linear Block Codes
On the Voronoi Neighbor Ratio for Binary Linear Block Codes
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DOI：
10.1109/18.737535
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发表时间：
1998-11
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影响因子：
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通讯作者：
E. Agrell
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文献类型：
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作者：
E. Agrell
分组码的软判决译码被认为是识别给定输入矢量所在的Voronoi区域的几何问题。提出了一种称为邻域比的度量方法，用来描述一个Voronoi区域有多少个面。给出了确定二元线性分组码邻区比的理论和算法，并给出了几种码型的结果。对长码的渐近分析表明，相邻比取决于码率是否小于1/2。对于低于该阈值的码字，所有码字对往往共享一个Voronoi面；对于较高的码率，相对较小的码字对共享一个Voronoi面。
Soft-decision decoding of block codes is regarded as the geometrical problem of identifying the Voronoi region within which a given input vector lies. A measure, called the neighbor ratio, is proposed to characterize how many facets a Voronoi region has. Theory and algorithms are presented to determine the neighbor ratio for binary linear block codes and results are given for several types of codes. An asymptotic analysis for long codes reveals that the neighbor ratio depends on whether the code rate is less than 1/2 or not. For rates below this threshold, all pairs of codewords tend to share a Voronoi facet; for higher rates, a relatively small fraction of them do.