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Polar codes Bhattacharyya parameter generalisation
IET Communications ( IF 1.6 ) Pub Date : 2020-07-02 , DOI: 10.1049/iet-com.2019.0950
Karim El‐Abbasy 1 , Ramy Taki ElDin 2 , Salwa Elramly 2 , Bassant Abdelhamid 2
Affiliation  

Recently, polar codes were proposed by Arikan to achieve optimum channel capacity given by Shannon theorem with low encoding and decoding complexity. Polar code construction depends on two main foundation criteria which are kernel matrix and Bhattacharyya parameter. They are related to each other, therefore the selection method for both affects the performance of polar code. Firstly, in this study, the derivations of the bounds for Bhattacharyya parameter are proved and generalised together with a proposed method to select the best kernel matrix to achieve the optimum capacity. Then, recursive channel transformations and successive cancellation decoding of the selected 3 × 3 best kernel matrix are proved. Furthermore, a general formula for polar code complexity and hardware implementation has been discussed. Simulation results show that the achievable bit error rate for the proposed methodology of selection is the same as some existing methods with the same order of complexity, which indicates its effectiveness. Polar code performance for the selected 3 × 3 best kernel matrix is improved as the code length increases. Moreover, this proposed method is general to be for higher dimension kernel matrices.

中文翻译:

极地代码Bhattacharyya参数概括

最近,Arikan提出了极性码来实现由Shannon定理给出的最佳信道容量,并且编码和解码复杂度较低。极地代码构造取决于两个主要基础标准,即内核矩阵和Bhattacharyya参数。它们彼此相关,因此两者的选择方法都会影响极性码的性能。首先,在本研究中,证明并推广了Bhattacharyya参数的边界的推导,并与提出的选择最佳核矩阵以实现最佳容量的方法一起推广。然后,证明了对选定的3×3最佳内核矩阵的递归通道变换和连续消除解码。此外,已经讨论了极性代码复杂性和硬件实现的通用公式。仿真结果表明,所提出的选择方法与某些现有方法具有相同的复杂度,其可达到的误码率相同,表明其有效性。随着代码长度的增加,所选3×3最佳内核矩阵的Polar代码性能将得到改善。此外,该方法通常适用于高维核矩阵。
更新日期:2020-07-03
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