On the Success Probability of the Box-Constrained Rounding and Babai Detectors

In communications, one frequently needs to detect a parameter vector \hbx in a box from a linear model. The box-constrained rounding detector \x^\sBR and Babai detector \x^\sBB are often used to detect \hbx due to their high probability of correct detection, which is referred to as success probability, and their high efficiency of implimentation. It is generally believed that the success probability P^\sBR of \x^\sBR is not larger than the success probability P^\sBB of \x^\sBB. In this paper, we first present formulas for P^\sBR and P^\sBB for two different situations: \hbx is deterministic and \hbx is uniformly distributed over the constraint box. Then, we give a simple example to show that P^\sBR may be strictly larger than P^\sBB if \hbx is deterministic, while we rigorously show that P^\sBR\leq P^\sBB always holds if \hbx is uniformly distributed over the constraint box.Comment: to appear in ISIT 201