Capacity-achieving rate-compatible polar codes

A method of constructing rate-compatible polar codes that are capacity achieving at multiple code rates with low-complexity sequential decoders is presented. The underlying idea of the construction exploits certain common characteristics of polar codes that are optimized for a sequence of successively degraded channels. The proposed code consists of parallel concatenation of multiple polar codes with information-bit divider at the input of each polar encoder. Thus, it is referred to as parallel concatenated polar (PCP) codes. A lower-rate PCP code is simply constructed by adding more constituent polar codes, which enables incremental retransmissions at different rates in order to adapt to channel conditions. Due to the length limitation of polar codes, the PCP code can only support a restricted set of rates that is characterized by the size of the kernel when conventional polar codes are used. To overcome this limitation, punctured polar codes, which provide more flexibility on blocklength by controlling a puncturing fraction, are considered as constituent codes. The existence of capacity-achieving punctured polar codes for any given puncturing fraction is proven. Using such punctured polar codes as constituent codes, it is shown that the proposed PCP code is capacity achieving for an arbitrary sequence of rates and for any class of degraded channels.

[1]  Ivana Maric,et al.  Capacity-achieving rate-compatible polar codes , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[2]  Jungwon Lee,et al.  HARQ Rate-Compatible Polar Codes for Wireless Channels , 2014, 2015 IEEE Global Communications Conference (GLOBECOM).

[3]  Alexander Vardy,et al.  List decoding of polar codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[4]  Steven W. McLaughlin,et al.  Rate-compatible puncturing of low-density parity-check codes , 2004, IEEE Transactions on Information Theory.

[5]  Kyeongcheol Yang,et al.  Design of Length-Compatible Polar Codes Based on the Reduction of Polarizing Matrices , 2013, IEEE Transactions on Communications.

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

[7]  Eren Sasoglu.  Polar Coding Theorems for Discrete Systems , 2011 .

[8]  Hossein Pishro-Nik,et al.  A practical approach to polar codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[9]  E. Arkan,et al.  A performance comparison of polar codes and Reed-Muller codes , 2008, IEEE Communications Letters.

[10]  Rüdiger L. Urbanke,et al.  The compound capacity of polar codes , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[11]  Keshab K. Parhi,et al.  Early Stopping Criteria for Energy-Efficient Low-Latency Belief-Propagation Polar Code Decoders , 2014, IEEE Transactions on Signal Processing.

[12]  Mikael Skoglund,et al.  Rate-Compatible LDPC Convolutional Codes Achieving the Capacity of the BEC , 2012, IEEE Transactions on Information Theory.

[13]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[14]  Kai Chen,et al.  Capacity-achieving rateless polar codes , 2015, 2016 IEEE International Symposium on Information Theory (ISIT).

[15]  Laurence B. Milstein,et al.  On the performance of hybrid FEC/ARQ systems using rate compatible punctured turbo (RCPT) codes , 2000, IEEE Trans. Commun..

[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]  Rongke Liu,et al.  A Novel Puncturing Scheme for Polar Codes , 2014, IEEE Communications Letters.

[18]  Emre Telatar,et al.  On the rate of channel polarization , 2008, 2009 IEEE International Symposium on Information Theory.

[19]  Kai Chen,et al.  A Hybrid ARQ Scheme Based on Polar Codes , 2013, IEEE Communications Letters.

[20]  Yan Chen,et al.  On the puncturing patterns for punctured polar codes , 2014, 2014 IEEE International Symposium on Information Theory.

[21]  Vera Miloslavskaya,et al.  Shortened Polar Codes , 2015, IEEE Transactions on Information Theory.

[22]  Aria Nosratinia,et al.  Rate-Compatible Short-Length Protograph LDPC Codes , 2013, IEEE Communications Letters.

[23]  Richard D. Wesel,et al.  Protograph-Based Raptor-Like LDPC Codes , 2014, IEEE Transactions on Communications.

[24]  Jilei Hou,et al.  Design of rate-compatible structured LDPC codes for hybrid ARQ applications , 2009, IEEE Journal on Selected Areas in Communications.

[25]  Joachim Hagenauer,et al.  Rate-compatible punctured convolutional codes (RCPC codes) and their applications , 1988, IEEE Trans. Commun..

[26]  Valerio Bioglio,et al.  Low-Complexity Puncturing and Shortening of Polar Codes , 2017, 2017 IEEE Wireless Communications and Networking Conference Workshops (WCNCW).