Optimum Polar Codes Encoder over Binary Discrete Memory-less Channels

In modern communication systems, there is an increasing need for more capacity-achieving coding schemes to fulfill high data rates demands. Polar codes are very promising candidates to achieve near Shannon's capacity and improved systems' reliability due to their polarized channel construction idea which depends on utilizing the good channel in data transmission and consumes the noisy ones in frozen bits transmission as pilots. This paper presented the performance of polar codes for binary-erasure-channel, binary-symmetric channel, and additive-white-Gaussian-noise-channel at various rates and different design parameter to find the optimum ones for these channels. The numerical analysis showed that when the rate increased the system bit error rate performance degrades, while it is improved when the design parameters are optimized for all the studied channels.