An exponential lower bound on the expected complexity of sphere decoding

The sphere decoding algorithm is an efficient algorithm used to solve the maximum likelihood detection problem in several digital communication systems. The sphere decoding algorithm has previously been claimed to have polynomial expected complexity. While it is true that the algorithm has an expected complexity comparable to that of other polynomial time algorithms for problems of moderate size it is a misconception that the expected number of operations asymptotically grow as a polynomial function of the problem size. In order to illustrate this point we derive an exponential lower bound on the expected complexity of the sphere decoder.

[1]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[2]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

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

[4]  Mohamed Oussama Damen,et al.  Lattice code decoder for space-time codes , 2000, IEEE Communications Letters.

[5]  M. O. Damen,et al.  Further results on the sphere decoder , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[6]  Inkyu Lee,et al.  A new reduced-complexity sphere decoder for multiple antenna systems , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[7]  Babak Hassibi,et al.  On the expected complexity of integer least-squares problems , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[8]  Babak Hassibi,et al.  High-rate codes that are linear in space and time , 2002, IEEE Trans. Inf. Theory.

[9]  Stephan ten Brink,et al.  Achieving near-capacity on a multiple-antenna channel , 2003, IEEE Trans. Commun..

[10]  Björn E. Ottersten,et al.  On the complexity of sphere decoding in digital communications , 2005, IEEE Transactions on Signal Processing.

[11]  Sergio Verdú,et al.  Computational complexity of optimum multiuser detection , 1989, Algorithmica.