标题： 关于对称二进制输入离散无记忆信道极化码的对称性 显示英文标题

标题： On the Symmetry of Polar Codes for Symmetric Binary-Input Discrete Memoryless Channels

摘要： 在本文中，我们研究对称二进制输入离散无记忆信道（B-DMC）上的极化码的对称性。 极化码的对称性属性最初在Arikan的工作中针对一般的B-DMC信道被指出。 借助这种对称性，输出向量$y_1^N$（$N$为块长度）可以根据其转移概率划分为等价类。 在本文中，我们提出了一个分析极化码在B-DMC信道上对称性的新框架。 提供了定理来描述接收向量之间的对称性。 显示英文摘要

摘要： In this paper, we study the symmetry of polar codes on symmetric binary-input discrete memoryless channels (B-DMC). The symmetry property of polar codes is originally pointed out in Arikan's work for general B-DMC channels. With the symmetry, the output vector $y_1^N$ ($N$ be the block length) can be divided into equivalence classes in terms of their transition probabilities. In this paper, we present a new frame of analysis on the symmetry of polar codes for B-DMC channels. Theorems are provided to characterize the symmetries among the received vectors.