Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization
Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization
复制标题
DOI：
10.1109/tit.2012.2228295
复制
发表时间：
2011-10
影响因子：
2.5
通讯作者：
Seyed Hamed Hassani;R. Mori;Toshiyuki TANAKA;R. Urbanke
中科院分区：
文献类型：
--
作者：
Seyed Hamed Hassani;R. Mori;Toshiyuki TANAKA;R. Urbanke
我们考虑了传输发生在二进制输入无记忆对称信道W上时，在大块长度区域中极化过程的渐近行为。特别地，我们研究了累积分布P（Zn ≤ z）的渐近性，其中{Zn}是与W相关的Bhattacharyya过程，以及它对传输率的依赖性。在此基础上，我们描述了渐进行为，以及它的依赖于速率，极化码的块错误概率使用连续消除解码器。这改进了Arıkan和Telatar的原始渐近界。我们的结果适用于基于l×l核矩阵的一般极化码。我们还提供了使用最大后验概率（MAP）解码器的极化码的块错误概率的渐近下界。当l = 2时，MAP下界和连续抵消上界一致，但是对于l > 2存在间隙。
We consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over a binary-input memoryless symmetric channel W. In particular, we study the asymptotics of the cumulative distribution P(Zn ≤ z), where {Zn} is the Bhattacharyya process associated with W, and its dependence on the rate of transmission. On the basis of this result, we characterize the asymptotic behavior, as well as its dependence on the rate, of the block error probability of polar codes using the successive cancellation decoder. This refines the original asymptotic bounds by Arıkan and Telatar. Our results apply to general polar codes based on l×l kernel matrices. We also provide asymptotic lower bounds on the block error probability of polar codes using the maximum a posteriori (MAP) decoder. The MAP lower bound and the successive cancellation upper bound coincide when l = 2, but there is a gap for l > 2.