"Bandwidth is a limited resource in modern communication systems, and to make the most efficient use of it, one needs to combine coding and modulation. Bit-interleaved coded modulation (BICM) is the newest design paradigm of bandwidth-efficient communication systems. Despite not being fully understood theoretically, BICM has been rapidly adopted in commercial systems such as wireless and wired broadband access networks, 3G telephony, ultrawideband transceivers, and digital video broadcasting. It will also be the de facto choice for most, if not all, future telecommunications standards.Nowadays, BICM systems are widely used, however, preliminary studies have revealed that they perform far from optimal. The objective of this proposal is to gain fundamental understandings about BICM systems and their building blocks. The rationale behind this proposal is that gaining a fundamental understanding of how the building blocks involved in a BICM system interact with each other will lead to improved designs.More particularly, in this project, we analyze the maximum transmission rates of BICM systems from two points of view. The first one analyzes this limit for an idealized transmission setup where the codewords are assumed to be infinitely long. The second approach analyzes this limit for systems that employ finite-length codewords. While the first case represent the ultimate maximum rate for BICM systems and it is interesting from a theoretical point of view, the second one is more relevant from a practical point of view since practical communication systems use finite-length codewords. The last part of this project deals with the design of BICM systems that approach these fundamental limits while maintaining an affordable complexity."