Convex relaxation based detection of binary data

The issue of binary data detection under subsampling condition is addressed in this work. Through convex relaxation, the original combinatorial optimization problem is transformed to an ℓ_∞ minimization problem which can be efficiently solved by ℓ_p approximation algorithm with sufficiently large p. Theoretical analysis and simulations indicate that when the number of sampled signals is around half of original binary vector, the reconstruction probability increases rapidly and gets close to 1. Compared with semidefinite programming algorithm, the convex relaxation based detection scheme has lower computational complexity while keeping similar reconstruction accuracy. Moreover, it is shown that ℓ_∞ is robust against additive noise.