Implementation of High Speed and Area Efficient Polar Encoder

Abstract

Polar codes were introduced by E.Ar?kan in 2008. They are the first family of error-correcting codes that attain the capacity of binary memoryless and symmetric channels with efficient encoding, decoding, and construction algorithms. In this paper, implementation of high speed and area efficient polar encoder for systematic polar codes is presented. According to an iterative property of the generator matrix and particular lower triangular structure of the matrix, the number of XOR computations are reduced. In this implementation, total area of the encoder is decreased by 33.69%, delay is decreased by 54.6% and power consumption is decreased by 39.44%.

Introduction

I. INTRODUCTION

Polar codes, originally proposed by Ar?kan [1], have gained enormous interest due to a number of distinctive features. For instance, polar codes have explicit coding structure and can achieve the capacity of Symmetric Binary Memoryless Channels (S-BMC). Moreover, polar codes with finite length yield competitive performance when compared to LDPC [2] and Turbo codes [3] in addition to having low encoding and decoding complexity. The standard polar codes are in nonsystematic form where both frozen bits and information bits (also referred to as user bits) are placed on the polarized bit-channels of the polarization structure and the user bits do not appear in the polar codeword. However, information bits as part of the codeword are required in some scenarios, such as the famous Turbo codes [4] whose component codes are systematic codes that can exchange information between modules in turbo decoding. To construct systematic polar codes (SPC), Ar?kan proposed the idea of shifting the user bits from polarized bit-channels to unpolarized bit-channels [5], which makes the frozen and user bits lie on two different extremes of polarization structure. Ar?kan showed that systematic polar codes outperform nonsystematic polar codes (NSPC) in terms of bit error rate (BER) and the performance have also been investigated in [6].

V. FUTURE SCOPE

The optimal polar encoding algorithm not only reduces the number of XOR computing units compared with the existing non-recursive algorithms, but also is beneficial to hardware implementation compared with the existing recursive algorithms.

Conclusion

Polar codes are considered as a major breakthrough in channel coding area as they achieve the maximum channel capacity. There are various methods of polar encoding. In this project we implemented a high speed and area efficient polar encoder , generated its area, power and delay reports. We have compared with existing low complexity polar encoder and observed that the implemented polar encoder has reduced area, power and delay. Area is decreased by 33.69% , Delay is decreased by 54.6% and power consumption is decreased by 39.44%.

References

[1] E. Arikan, Channel Polarization: A method for constructing capacity achieving codes for symmetric Serbian-input memoryless channels. IEEE Trans. Inf. Theory 55, 3051–3073 ,2009 . [2] E. Arikan, Systematic polar coding. IEEE Commun Lett 15(8), 860– 862 ,2011 . [3] H. Vangala, Y. Hong, E. Viterbo, Efficient algorithms for systematic polar encoding. IEEE Commun Lett 20(1),17–20 ,2016 . [4] G. TaiChen, Z. Zhaoyang, Z. Caijun, Z. Liang, A low complexity encoding algorithm for systematic polar codes. IEEE Commun Lett 20(7), 1277–1280 ,2016 .

Copyright

Copyright © 2024 Dr. K. Usha, Dr. Vibha D. Kulkarni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.