Polarization improves E0
Polarization improves E0
复制标题
偏振改善E0
DOI：
10.1109/tit.2014.2309679
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
E. Telatar
中科院分区：
文献类型：
--
作者：
Mine Alsan;E. Telatar
我们证明，通过 Arikan 的偏振变换进行通道组合和分裂可以提高二进制输入通道的 Gallager 可靠性函数 E0。从这个意义上说，极化“创造”了E0。这一观察结果为为什么极坐标变换产生容量实现和低复杂性代码提供了另一个理由：E0 的改进转化为复杂性-错误-概率权衡的改进。在分析极化码时，人们会检查随着底层通信信道经历一系列转换而遵循信息度量演变的辅助随机过程。本文的结论表明，与此类分析相关的 E0 过程是一个下鞅。
We prove that channel combining and splitting via Arikan's polarization transformation improves Gallager's reliability function E0 for binary input channels. In this sense polarization `creates' E0. This observation gives yet another justification as to why the polar transform yields capacity achieving and low complexity codes: the improvement in E0 translates to an improvement in complexity-error-probability trade-off. In analyzing polar codes, one examines auxiliary random processes that follow the evolution of information measures as an underlying communication channel undergoes a sequence of transformations. The conclusion of this paper shows that the E0 process associated to such an analysis is a submartingale.