高斯信道下极化码的子信道错误概率计算

Calculation of Sub-Channel's Error Probability of Polar Code under AWGN Channel

极化码作为一种信道容量可达的信道编码方法,最初由Arikan在2008年正式提出,极化码指经信道极化变换后得到的极化信道呈两极分化,一部分信道表现出无噪信道的特征,另外一部分信道表现出纯噪信道的特征,将需要传输的信息在"无噪信道"上传输,剩下的信道传输发收方均已知的比特。当码长很长时,信道容量可达,因此,在极化码中如何选出"无噪信道"来传输有用信息是极化码中的关键技术之一。然而目前研究中,极化码在二进制输入离散无记忆信道(BDMC)下,衡量子信道好坏的参数计算方法和复杂程度因具体信道类型的不同而不同,除了二进制删除信道(BEC),其他BDMC信道很难通过简单的迭代公式计算得到优质信道。目前二进制输入高斯信道(BI-AWGN)利用高斯逼近算法,能计算出极化码在高斯信道下子信道传输错误概率,从而得到所需的"无噪信道"。介绍极化码在二进制输入高斯信道(BI-AWGN)下,分别将二分法、线性插值法和多项式拟合法引入到高斯逼近算法中,简化子信道错误概率的计算过程。仿真表明,二分法、线性插值法和多项式拟合在信息位的选择上能简化计算,同时有较好的性能。

As a method of channel coding that can achieve the channel＇s capacity, polar code was proposed by Arikan in 2008. With the transformation of channel polarization, we can obtain a series of polarized channels. A part of the channels have the characteristic of noiseless channel and the other part of the channels seem to be pure noise channels. We prefer to transmit the information bits on those noiseless channels and transmit bits that are known by the transmitter and receiver. When the length of the code becomes very large, the channel can achieve its capacity. Therefore it＇s a key point in polar code to find those noise- less channels. Polar code is sensitive to the type of channel, so it will make differences in different channels to calculate the pa- rameters to measure the quality of the sub-channels. Besides binary erasure channel, the other types of BDMC are hard to find good channels by simple iterative formulas. With the help Gaussian approximation algorithm, we can calculate the channel＇ s transmission error probability and then obtain the noiseless channels. In this paper, we combine with bi-search, linear interpo- lation and poly-fitting to simplifiy the process of calculation. The simulation shows that those methods perform well in selecting the information bits.