Monte Carlo Simulation of the Non-Systematic and Systematic Polar Codes

Abstract

To recreate the sent signal, we have spent the last few decades looking for methods that will decrease the effect of noise to a considerable amount. A brand-new idea created by Erdal Arikan is known as polar codes. The 3GPP standardized the polar codes for correcting the errors in the 5G control channels due to its unique property of splitting the channel into good and bad channels according to the channel polarization concept. Polar codes are error correction codes that increase channel capacity and are more appealing and effective due to their lower level of complexity. This paper aimed to compare the Bit Error Rate (BER) and Frame Error Rate (FER) performance of the Non-Systematic Polar codes (NSPC) and Systematic Polar codes (SPC), along with also comparing the two most commonly used decoding techniques (like Successive Cancellation and Successive Cancellation List) of the NSPC. The Systematic and Non-Systematic Polar codes have been implemented on the MATLAB tool over a block length of 1024 with a 1/2 rate, and their BER and FER have been calculated. The SPC leads in the error correction performance with N*log <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> N complexity compared to NSPC, with (N/2)*log <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> N Complexity. The simulated result also shows that the Successive Cancellation List (SCL) enhances the performance of the Successive Cancellation (SC) with increasing list size, but complexity also increases by a factor of L. The SCL decoding of the NSPC decoder with list size 32 performs better than the SC decoding of the SPC at a value of one E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</inf> /No(dB).