Upper bounds on the performance of maximum-likelihood decoded binary block codes in AWGN and block fading channels

In this dissertation, different bounding techniques (with emphasis on upper bounds) have been studied. More specifically, Gallager's First Bounding Technique (GFBT) has been fully investigated. Several upper bounds based on GFBT have been analyzed. Within the framework of GFBT, Tangential Sphere Bound (TSB) had been shown to be the tightest upper bound on the block error probability of ML decoded binary block codes. TSB uses GFBT together with the well-known union bound which is the simplest inequality from the large class of so-called Bonferroni-type inequalities in probability theory. In this work, a family of second-order Bonferroni-type inequalities is studied and based on GFBT and such inequalities, an upper bound on the block error probability of spherical codes in Additive White Gaussian Noise (AWGN) channel is proposed. The initial resulting bound is rather complicated as it requires the global geometrical properties of the code. The bound is shown to be tighter than TSB and hence is the tightest upper bound on the ML performance of spherical constellations. (Abstract shortened by UMI.)...