Information-theoretic and genie-aided analyses of random-acess algorithms

The random-access problem is one of organizing a population of users so that they may efficiently share the resources of a single communications channel. In this thesis, the identification of information which must be ex¬ changed within a set of infinitely many, uncoordinated users possibly attempting to access a common collision-type channel, is explicitly ad¬ dressed. Particularly, the essential information being gathered in a col¬ lision resolution algorithm to successfully transmit the messages of the users, is specified. This is the first time in the literature where pure in¬ formation-theoretic arguments were used to describe random-accessing systems and are applied to calculate the performance of specific pro¬ tocols. Moreover, information-theoretic bounds are applied to ternary feedback to yield an upper bound on the maximal stable throughput of a random access broadcast channel; multiplicity feedback is discussed as well. Nonetheless, this concept still offers interesting unanswered aspects to find the capacity of the collision channel with feedback. The problem of resolving collisions is then viewed as a generic search problem with N independent random variables, e.g., active users, where the concept of a probabilistic genie is introduced and the capacity for the first non-trivial case, namely N = 3 collided packets, where N is known to all users, is given. For N = 4 new lower and upper bounds on the efficiency are derived. Unfortunately, they do not meet each other such that the capacity for N > 4 users is still an open problem. Furthermore, various facets of selected problems applying different degrees of feedback are considered. For binary feedback, in particular