A comparison of Polar Code Constructions and Punctur-ing methods for AWGN and Fading channels

Abstract: Today 5G and other wireless standards are being developed for the future of our society. The different use-cases of future wireless services are going to be ever-more demanding, whether it is vehicular communication or low-powered sensor networks. High-rate, ultra-reliable and low-power are future requirements that will also affect the coding schemes being used. A relatively recent coding scheme, called polar codes, has the potential to fulfill all of these requirements if the coding scheme applied is well-designed. In this thesis we will be focusing on practical algorithms for implementation of polar codes at medium-sized block-lengths.       Polar codes are very different from other modern coding schemes. The code construction is rather unique in that they are dependent on the underlying channel, where the code construction can change with the Signal-to-Noise-Ratio of the AWGN channel. The puncturing of polar codes is also non-trivial compared to other coding schemes. Since the Polar Codes are dependent on the underlying channel, the fading channel performance is thus important to consider. In this thesis we aim to show through simulations how these different concepts affect the Block Error Rate (BLER) performance. Specifically, we compare how code constructions compare over the AWGN channel, how code construction affects the BLER performance with puncturing and how puncturing affects the performance over fading channels. We find that an appropriate code construction is very important for optimal performance over the AWGN channel with puncturing, in our case using Gaussian Approximation. We also find that different puncturing methods have vastly different performances for different rates over the AWGN and Rayleigh fading channel and that applying an interleaver is very important for optimal performance.