Polar codes for q-ary channels, q =2r
Polar codes for q-ary channels, q =2r
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DOI：
10.1109/isit.2012.6283741
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发表时间：
2011-07
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通讯作者：
Woomyoung Park;A. Barg
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文献类型：
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作者：
Woomyoung Park;A. Barg
我们研究极化的非二进制信道的输入字母大小q = 2 r，r = 2，3，.利用Arikan的极化核H2，我们证明了极化过程中产生的虚拟信道收敛到容量为1，2，.的q元信道，r比特，并且总传输速率接近信道的对称容量。这导致用于q元信道的显式传输方案。使用连续消除的解码的错误概率表现为exp（-Nα），其中N是码长，α是小于0.5的任何常数。
We study polarization for nonbinary channels with input alphabet of size q = 2r, r = 2,3,.... Using Arikan's polarizing kernel H2, we prove that virtual channels that arise in the process of polarization converge to q-ary channels with capacity 1,2,..., r bits, and that the total transmission rate approaches the symmetric capacity of the channel. This leads to an explicit transmission scheme for q-ary channels. The error probability of decoding using successive cancellation behaves as exp(-Nα), where N is the code length and α is any constant less than 0.5.