On the Randomized Babai Point

Estimating the integer parameter vector in a linear model with additive Gaussian noise arises from many applications, including communications. The optimal approach is to solve an integer least squares (ILS) problem, which is unfortunately NP-hard. Recently Klein’s randomized algorithm, which finds a sub-optimal solution to the ILS problem, to be referred to as the randomized Babai point, has attracted much attention. This paper presents a formula of the success probability of the randomized Babai point and some interesting properties, and compares it with the deterministic Babai point.