Essay Example on Polar codes have been considered as an Important Breakthrough









Polar codes have been considered as an important breakthrough in information theory mainly due to the fact that they are capable of achieving capacity with its explicit construction and low encoding and decoding complexity Polar codes are based on a novel concept of channel polarization introduced by Erdal Arikan Being probably the first-ever capacity-achieving codes polar codes have attracted increasing attention from both academia and industries That is why they have been selected as one of the most promising channel codes for the next-generation telecommunications standard 5G Let us consider a binary input discrete memoryless symmetric BI DMS channel The Channel Polarization technique creates N synthesized channels out of N identical copies of the given BI DMS channel The recursive structure of this transform manufactures polarized channels as N in the sense that they are either perfect or useless but nothing in between Once all channels get polarized there is no need to code anymore as one can directly transmit information bits over the perfect channels and dummy bits over the useless ones Although belonging to family of capacity-achieving codes with low encoding and decoding complexity polar codes suffer from certain drawbacks in practice 

As in order to achieve error rates suitable for practical applications the block lengths have to be very large The implementation of traditional successive cancellation SC decoder suffers from a very high latency at these block lengths and hence the corresponding decoder algorithm experiences increase in its computational complexity The classic SC decoder follows a recursive divide and conquer approach which reduces the problem of decoding a length N polar code into the decoding of two N 2 constituent codes However these decodings are not independent as the input to the second decoder relies on the output of the first one thus introducing significant latency Addressing to this issue a new SC list decoding algorithm is proposed for polar codes in which performs better than the traditional SC decoder The idea employed in is to keep track of L survival paths concurrently instead of keeping only one survival path as that exists in classical decoders 

This results in narrowing the performance gap between sub-optimal SC decoder and optimal maximum likelihood ML or maximum a posteriori MAP decoder Apart from this the only drawback to this approach is the list size L which increases the decoding complexity Also in order to achieve the expected performance for practical applications it has been found out that L must be kept high Obviously increasing L directly for better performance can not be appreciated

To this end an adaptive SC list decoder has been proposed in which talked about downsizing of list size In order to improve the low minimum distance of polar codes the concatenation of polar codes with Cyclic Redundancy Check CRC error correcting technique is also proposed in which has outperformed a more matured current state of art LDPC codes with a simple concatenation scheme of polar code 2048 1024 with a 16 bit CRC using the SC list decoding The fixed list size L in SCL decoder during the entire decoding process could not make any necessary size adaption to fit the application requirements on either decoding performance or computational complexity This work is inspired by the above problem in the existing SC list decoder To address this issue in this thesis a novel efficient SC list decoding algorithm has been proposed Unlike the existing fixed list size method in this approach will downsize the list size by taking concept of reliable bits into consideration at each decoding stage Simulation results have shown that this proposed approach can effectively shrink the required list size and yields very similar performance as the current state of art SC list decoder in Reduction in time complexity is an added advantage 

The rest of this thesis is organized as follows Section II reviews preliminary discussions on the existing SC decoder and SC list decoder Section III proposes the improved efficient SC list decoder based on reliability parameters The simulation results based on the proposed SC list decoder have been included in the Section V Section VI concludes the entire thesis and fosters up the direction of future works II PRELIMINARIES A Conventional SC Decoder The SC decoder has been given by Arikan in Because of its low O log N complexity it has been accepted as the classical decoding algorithm by all polar codes researchers Let the polar code of our interest is of length N and rate of information R and number of information bits transmitted in a single frame length is K As per the definition R K N the number of frozen bits is N K We denote indices of these frozen bits by F and information bits vector by

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