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Extremal Channels of Gallager's $E_{0}$ Under the Basic Polarization Transformations

机译:基本极化转换下加拉格尔$ E_ {0} $的极端通道

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摘要

We study the extremality of the binary erasure channel and the binary symmetric channel for Gallager's reliability function $E_{0}$ of binary input discrete memoryless channels evaluated under the uniform input distribution from the aspect of channel polarization. In particular, we show that amongst all binary discrete memoryless channels of a given $E_{0}(rho)$ value, for a fixed $rhogeq 0$, the binary erasure channel and the binary symmetric channel are extremal in the evolution of $E_{0}$ under the one-step polarization transformations.
机译:我们从通道极化的角度研究了在均匀输入分布下评估的二进制输入离散无记忆通道的Gallager可靠性函数$ E_ {0} $的二进制擦除通道和二进制对称通道的极值。特别地,我们表明,在给定的$ E_ {0}(rho)$值的所有二进制离散无内存通道中,对于固定的$ rhogeq 0 $,二进制擦除通道和二进制对称通道在$的演化中是极端的一步极化转换下的E_ {0} $。

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