2014/10/19 by Jinming Wen, Wen, Jinming, Xiao-Wen Chang +1
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.1410.5040
openalex publication_date 2014/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In many applications including communications, one may encounter a linear model where the parameter vector \hbx is an integer vector in a box. To estimate \hbx, a typical method is to solve a box-constrained integer least squares (BILS) problem. However, due to its high complexity, the box-constrained Babai integer point \x^\sBB is commonly used as a suboptimal solution. In this paper, we first derive formulas for the success probability P^\sBB of \x^\sBB and the success probability P^\sOB of the ordinary Babai integer point \x^\sOB when \hbx is uniformly distributed over the constraint box. Some properties of P^\sBB and P^\sOB and the relationship between them are studied. Then, we investigate the effects of some column permutation strategies on ¶^\sBB. In addition to V-BLAST and SQRD, we also consider the permutation strategy involved in the LLL lattice reduction, to be referred to as LLL-P. On the one hand, we show that when the noise is relatively small, LLL-P always increases P^\sBB and argue why both V-BLAST and SQRD often increase P^\sBB; and on the other hand, we show that when the noise is relatively large, LLL-P always decreases P^\sBB and argue why both V-BLAST and SQRD often decrease P^\sBB. We also derive a column permutation invariant bound on P^\sBB, which is an upper bound and a lower bound under these two opposite conditions, respectively. Numerical results demonstrate our findings. Finally, we consider a conjecture concerning \x^\sOB proposed by Ma et al. We first construct an example to show that the conjecture does not hold in general, and then show that it does hold under some conditions.