Fast Encoding of Polar Codes With Reed–Solomon Kernel

A low-complexity systematic encoding algorithm for polar codes with Reed-Solomon (RS) kernel is presented. The proposed method relies on fast Fourier transform-based RS encoding techniques. An application of polar codes in storage systems is considered.

[1]  Martin Bossert,et al.  Channel Coding for Telecommunications , 1999 .

[2]  Martin Bossert,et al.  On the equivalence of generalized concatenated codes and generalized error location codes , 2000, IEEE Trans. Inf. Theory.

[3]  Mario Blaum,et al.  Sector-Disk (SD) Erasure Codes for Mixed Failure Modes in RAID Systems , 2014, TOS.

[4]  Peter Trifonov,et al.  A Method for Fast Computation of the Fourier Transform over a Finite Field , 2003, Probl. Inf. Transm..

[5]  Yi Hong,et al.  Efficient Algorithms for Systematic Polar Encoding , 2016, IEEE Communications Letters.

[6]  Daniel J. Costello,et al.  Polynomial weights and code constructions , 1973, IEEE Trans. Inf. Theory.

[7]  Sandro Bellini,et al.  On the Structure of Cyclotomic Fourier Transforms and Their Applications to Reed-Solomon Codes , 2011, IEEE Transactions on Communications.

[8]  Alexander Vardy,et al.  Flexible and Low-Complexity Encoding and Decoding of Systematic Polar Codes , 2016, IEEE Transactions on Communications.

[9]  Peter Trifonov,et al.  Low-Complexity Implementation of RAID Based on Reed-Solomon Codes , 2015, TOS.

[10]  Peter Trifonov,et al.  Efficient Design and Decoding of Polar Codes , 2012, IEEE Transactions on Communications.

[11]  Robert F. H. Fischer,et al.  Multilevel codes: Theoretical concepts and practical design rules , 1999, IEEE Trans. Inf. Theory.

[12]  Jungwon Lee,et al.  Performance Limits and Practical Decoding of Interleaved Reed-Solomon Polar Concatenated Codes , 2013, IEEE Transactions on Communications.

[13]  Jungwon Lee,et al.  Fast multi-dimensional polar encoding and decoding , 2014, 2014 Information Theory and Applications Workshop (ITA).

[14]  T. Moon.  Error Correction Coding: Mathematical Methods and Algorithms , 2005 .

[15]  Chris Heegard,et al.  On Hyperbolic Cascaded Reed-Solomon Codes , 1993, AAECC.

[16]  Erdal Arikan,et al.  Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels , 2008, IEEE Transactions on Information Theory.

[17]  R. Blahut.  Theory and practice of error control codes , 1983 .

[18]  Erold W. Hinds,et al.  Error-correction coding , 1996 .

[19]  Peter Trifonov,et al.  On the additive complexity of the cyclotomic FFT algorithm , 2012, 2012 IEEE Information Theory Workshop.

[20]  Mingqiang Li,et al.  STAIR Codes: A General Family of Erasure Codes for Tolerating Device and Sector Failures , 2014, TOS.

[21]  Jungwon Lee,et al.  Compound polar codes , 2013, 2013 Information Theory and Applications Workshop (ITA).

[22]  Erdal Arikan,et al.  Systematic Polar Coding , 2011, IEEE Communications Letters.

[23]  Toshiyuki Tanaka,et al.  Source and Channel Polarization Over Finite Fields and Reed–Solomon Matrices , 2012, IEEE Transactions on Information Theory.

[24]  Rüdiger L. Urbanke,et al.  Polar Codes for Channel and Source Coding , 2009, ArXiv.

[25]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[26]  Toshiyuki Tanaka,et al.  Non-binary polar codes using Reed-Solomon codes and algebraic geometry codes , 2010, 2010 IEEE Information Theory Workshop.

[27]  Caijun Zhong,et al.  A Low Complexity Encoding Algorithm for Systematic Polar Codes , 2016, IEEE Communications Letters.

[28]  Peter Trifonov,et al.  Binary successive cancellation decoding of polar codes with Reed-Solomon kernel , 2014, 2014 IEEE International Symposium on Information Theory.

[29]  Norbert Stolte,et al.  Rekursive Codes mit der Plotkin-Konstruktion und ihre Decodierung , 2002 .

[30]  Elena Costa,et al.  On computing the syndrome polynomial in Reed-Solomon decoder , 2004, Eur. Trans. Telecommun..

[31]  Peter Trifonov,et al.  Matrix-Vector Multiplication via Erasure Decoding , 2007 .