Hide/Show Apps

Polar codes: performance over fading channels and convergence to reed-muller codes

Download
2019
Özvarış, Irmak
Polar codes introduced in 2008 by Erdal Arıkan have been proven to achieve Shannon capacity for any binary-input discrete memoryless channel. Being adopted as a part of the official coding scheme for the 5G standard, up-to-date research has moved from theory to practical applications, albeit keeping the connection with its ancestors. This thesis aims to address these two topics, narrowing down firstly to the performance of polar codes on fading binary symmetric channels and then to the relationship between polar codes and Reed-Muller codes. For fading channels, we experiment on a hierarchical scheme proposed in 2014 by Si, Köylüoğlu and Viswanath that uses multiple polar coding phases. We simulate the two-state fading case that utilizes three polar codes; two of them designed for binary symmetric channels and one for a binary erasure channel with an erasure rate representing the fading probability. We compare the bit error ratio performance of the proposed scheme with original polar coding. Results show that the hierarchical scheme outperforms the other whenever the probability of being in the degraded channel is not very high. As for the comparison between polar and Reed-Muller codes, we primarily focus on the generator matrices of the two codes constructed for binary erasure and additive white Gaussian noise channels. Motivated by the convergence proof of Mondelli; we present some observations asserting the convergence thresholds of polar codes to Reed-Muller codes, in terms of the channel parameters such as erasure probability or signal to noise ratio.