Multilevel polarization of polar codes over arbitrary discrete memoryless channels
Multilevel polarization of polar codes over arbitrary discrete memoryless channels
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任意离散无记忆通道上极化码的多级极化
DOI：
10.1109/allerton.2011.6120375
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
S. Sandeep Pradhan
中科院分区：
文献类型：
--
作者：
A. G. Sahebi;S. Sandeep Pradhan
结果表明，原始极化码结构足以实现任意输入字母大小的离散无记忆信道的对称容量。结果表明，一般情况下，通道极化发生在几个而不是两个水平上，因此合成的通道要么是无用的，要么是完美的，要么是“部分完美的”。给定输入字母的协集分解，存在对应的部分完美信道，其输出唯一地确定信道输入符号所属的协集。通过对编码和解码规则的轻微修改，表明某些信息字母在部分完美信道上的完美传输是可能的。通过实例表明，在任意信道上，极坐标码不能达到协集码的容量。
It is shown that the original construction of polar codes suffices to achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two, levels so that the synthesized channels are either useless, perfect or “partially perfect”. Given a coset decomposition of the input alphabet, there exists a corresponding partially perfect channel whose outputs uniquely determine the coset where the channel input symbol belongs to. By a slight modification of the encoding and decoding rules, it is shown that perfect transmission of certain information letters over partially perfect channels is possible. It is also shown through an example that polar codes do not achieve the capacity of coset codes over arbitrary channels.