Efficient sphere decoding of polar codes

The performance of the original successive cancellation decoder of short-length polar codes is inferior to that of the maximum-likelihood decoder. Existing sphere decoding algorithms of polar codes have a high computational complexity even for short lengths. This is because, when exploring the tree defined by the generator matrix of the code, existing algorithms employ loose branching conditions and end up visiting many more nodes than needed. We propose improved branching conditions that significantly reduce the search complexity. A simple example reports an improvement of two orders of magnitude at Eb over N0 = 4 dB compared to the standard sphere decoders.

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

[2]  Georgios B. Giannakis,et al.  Sphere decoding algorithms with improved radius search , 2005, IEEE Trans. Commun..

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

[4]  Giuseppe Caire,et al.  A unified framework for tree search decoding: rediscovering the sequential decoder , 2005, IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, 2005..

[5]  Babak Hassibi,et al.  On the sphere-decoding algorithm II. Generalizations, second-order statistics, and applications to communications , 2005, IEEE Transactions on Signal Processing.

[6]  Giuseppe Caire,et al.  A unified framework for tree search decoding: rediscovering sequential decoding , 2005, IEEE Information Theory Workshop, 2005..

[7]  Babak Hassibi,et al.  Performance of sphere decoding of block codes , 2006, IEEE Transactions on Communications.

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

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

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

[11]  Babak Hassibi,et al.  On the Performance of Sphere Decoding of Block Codes , 2009, 2006 IEEE International Symposium on Information Theory.

[12]  John R. Barry,et al.  Polar codes for partial response channels , 2013, 2013 IEEE International Conference on Communications (ICC).

[13]  Paul H. Siegel,et al.  Enhanced belief propagation decoding of polar codes through concatenation , 2014, 2014 IEEE International Symposium on Information Theory.

[14]  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.

[15]  Giuseppe Caire,et al.  On maximum-likelihood detection and the search for the closest lattice point , 2003, IEEE Trans. Inf. Theory.

[16]  Emanuele Viterbo,et al.  A universal lattice code decoder for fading channels , 1999, IEEE Trans. Inf. Theory.

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

[18]  M. O. Damen,et al.  A unified framework for tree search decoding: rediscovering the sequential decoder , 2005, SPAWC 2005.

[19]  Claus-Peter Schnorr,et al.  Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems , 1991, FCT.

[20]  Babak Hassibi,et al.  A branch and bound approach to speed up the sphere decoder , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[21]  Emanuele Viterbo,et al.  Folded tree maximum-likelihood decoder for Kronecker product-based codes , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

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