Implementation of Polar Codes over AWGN and Binary Symmetric Channel

Abstract

Objectives: Forward Error Correction (FEC) is a mechanism that has been used for years to improve the reliability of digital communications over wireless channels as they are subjected to interference, fading and noise. The goal of FEC is to add some redundant data to the input stream which facilitates the receiver to recognize and correct the errors with no need of sender to transmit the data again. In this paper we have computed bit error rate using polar codes in an Additive White Gaussian Noise Channel (AWGN) and Binary Symmetric Channel (BSC) at different block lengths. Methods/Analysis: Shannon limit states that it is the maximum amount of information that any given channel can carry. Latterly, there have been inventions in Forward Error Correction (FEC) area that allows today's systems to approach the Shannon limit. One such advancement in FEC is Polar Codes which has mathematically proved to attain the Shannon capacity for Binary Discrete Memoryless Channels using the phenomenon of channel polarization which states that by recursively combining and splitting N individual channels, some channels will become completely noiseless and some become noisy. These noiseless channels are then chosen to send information bits. Findings: We have implemented polar codes over BIAWGN and BSC and have calculated their bit error rate's at different channel ranges. The decoder used for decoding polar codes is successive cancellation decoder and it's seen that the performance is not that good at small block lengths but as the block length increases the performance improves when compared with the un-coded data stream. Applications: As polar codes are the first codes that achieve the Shannon capacity, so they seem to be the best solution for discrete memoryless channels which encounter packet failures and other noisy disturbances. Also, apart from channel encoding, polar codes found its applications in lossy and lossless source coding, coding for secrecy, communication over multiple access channels.