An Efficient Software List Sphere Decoder for Polar Codes

Polar codes, first achieving the capacity of symmetric binary-input discrete memoryless channels (B-DMCs), have been standardized for eMBB control channels. Since 5G cellular requires flexible architecture which is realized by the software defined networking paradigm, efficient polar decoder is anticipated. Though successive cancellation list (SCL) decoder achieves satisfactory performance, it requires a large amount of memory. For short control channel codes, sphere decoder (SD) is an alternative, but costs unbearable time complexity at low signal-to-noise ratio. List sphere decoder (LSD) abandons the radius and keeps a list of best paths to gain a fixed complexity. However, LSD needs a large list size L for satisfactory performance. In this paper, an efficient software LSD with path pruning and efficient sorting is proposed. We recall the radius as the bound to delete the paths out of the sphere at very early levels. Since L is dynamic, efficient sorting is proposed to reduce the copy operations. Implemented with C++ , the proposed decoder can reduce up to 65.3 % latency compared with the original LSD, with the same performance and lower complexity.

[1]  Keshab K. Parhi,et al.  Low-Latency Sequential and Overlapped Architectures for Successive Cancellation Polar Decoder , 2013, IEEE Transactions on Signal Processing.

[2]  Xiaohu You,et al.  Segmented CRC-Aided SC List Polar Decoding , 2016, 2016 IEEE 83rd Vehicular Technology Conference (VTC Spring).

[3]  U. Fincke,et al.  Improved methods for calculating vectors of short length in a lattice , 1985 .

[4]  Kai Chen,et al.  Low-Complexity Sphere Decoding of Polar Codes Based on Optimum Path Metric , 2013, IEEE Communications Letters.

[5]  Alexander Vardy,et al.  List Decoding of Polar Codes , 2015, IEEE Transactions on Information Theory.

[6]  Warren J. Gross,et al.  Matrix reordering for efficient list sphere decoding of polar codes , 2016, 2016 IEEE International Symposium on Circuits and Systems (ISCAS).

[7]  Xiaohu You,et al.  Low-latency software successive cancellation list polar decoder using stage-located copy , 2016, 2016 IEEE International Conference on Digital Signal Processing (DSP).

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

[9]  Xiaohu You,et al.  Joint List Polar Decoder with Successive Cancellation and Sphere Decoding , 2018, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

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

[11]  Jing Guo,et al.  Efficient sphere decoding of polar codes , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[12]  Michael E. Pohst,et al.  On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications , 1981, SIGS.

[13]  Warren J. Gross,et al.  A Semi-Parallel Successive-Cancellation Decoder for Polar Codes , 2013, IEEE Transactions on Signal Processing.

[14]  Babak Hassibi,et al.  On the sphere-decoding algorithm I. Expected complexity , 2005, IEEE Transactions on Signal Processing.

[15]  Warren J. Gross,et al.  A Fast Polar Code List Decoder Architecture Based on Sphere Decoding , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Xiaohu You,et al.  An Improved Software List Sphere Polar Decoder With Synchronous Determination , 2019, IEEE Transactions on Vehicular Technology.

[17]  Warren J. Gross,et al.  List sphere decoding of polar codes , 2015, 2015 49th Asilomar Conference on Signals, Systems and Computers.

[18]  Konstantinos Nikitopoulos,et al.  Reduced Latency ML Polar Decoding via Multiple Sphere-Decoding Tree Searches , 2018, IEEE Transactions on Vehicular Technology.

[19]  Alexander Vardy,et al.  How to Construct Polar Codes , 2011, IEEE Transactions on Information Theory.

[20]  Mehmet Ertugrul Çelebi,et al.  Code based efficient maximum-likelihood decoding of short polar codes , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[21]  Warren J. Gross,et al.  Fast and Flexible Successive-Cancellation List Decoders for Polar Codes , 2017, IEEE Transactions on Signal Processing.

[22]  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.