Extremality Between Symmetric Capacity and Gallager’s Reliability Function $E_{0}$ for Ternary-Input Discrete Memoryless Channels
Extremality Between Symmetric Capacity and Gallager’s Reliability Function $E_{0}$ for Ternary-Input Discrete Memoryless Channels
复制标题
三态输入离散无记忆通道的对称容量与 Gallager 可靠性函数 $E_{0}$ 之间的极值
DOI：
10.1109/tit.2017.2751500
复制
发表时间：
2018
影响因子：
2.5
通讯作者：
Iwata Ken-ichi
中科院分区：
文献类型：
--
作者：
Sakai Yuta;Iwata Ken-ichi
本文研究了均匀输入分布下三输入离散无记忆信道（T-DMC）的对称容量和Gallager可靠性函数E0之间的精确范围。我们首先推导出两个极端的三输入强对称信道的E0函数的最大值和最小值之间的所有三输入强对称信道具有固定的容量。扩展了三输入强对称信道的结果，我们第二次推导出三输入Gallager对称信道的容量和E0函数之间的精确范围。第三，我们证明了T-DMC的对称容量和E0函数之间的精确范围与三元输入Gallager对称信道的范围相一致。特别是，我们确定的极值信道采取的最大值和最小值E0之间的所有T-DMC与一个固定的对称容量。作为结果的应用，我们描述了具有固定对称容量的T-DMC的误差指数的一些界。
This paper examines the exact ranges between the symmetric capacity and Gallager's reliability function E0for ternary-input discrete memoryless channels (T-DMCs) under a uniform input distribution. We first derive the two extremal ternary-input strongly symmetric channels taking the maximum and minimum values of the E0function among all ternary-input strongly symmetric channels with a fixed capacity. Extending the results of ternary-input strongly symmetric channels, we second derive the exact ranges between capacity and the E0function for ternary-input Gallager-symmetric channels. We third show that the exact ranges between the symmetric capacity and the E0function of T-DMCs coincide with the ranges of ternaryinput Gallager-symmetric channels. In particular, we identify the extremal channels taking the maximum and minimum of E0among all T-DMCs with a fixed symmetric capacity. As applications of the results, we describe some bounds of error exponents for T-DMCs with a fixed symmetric capacity.