NDLI: Polar codes Bhattacharyya parameter generalisation

Content Provider	IET Digital Library
Author	Abbasy, Karim El Din, Ramy Taki El Elramly, Salwa Abdelhamid, Bassant
Abstract	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.
Starting Page	1718
Ending Page	1729
Page Count	12
ISSN	17518628
Volume Number	14
e-ISSN	17518636
Issue Number	Issue 11, Jul (2020)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-com/14/11
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-com.2019.0950
Journal	IET Communications
Publisher Date	2020-03-17
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Achievable Bit Error Rate Algebra Bhattacharyya Parameter Generalisation Channel Capacity Channel Coding Code Decoding Encoding Error Statistics High Dimension Kernel Matrix Matrix Algebra Optimum Channel Capacity Polar Code Complexity Polar Code Construction Performance Recursive Channel Transformations Shannon Theorem Statistics Successive Cancellation Decoding Complexity
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Computer Science Applications

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