Diversity embedding for broadband communication

Given uncertainty in environment, a conservative approach is to design for the worst case, leading to a game-theoretic situation where the environment is controlled by an adversary. However, in many cases, the uncertainty arises from randomness, not an adversary. Wireless fading channels are an example of such a system, where the random fading causes uncertainty (at the transmitter) about rates supported by the channel. The question asked in the thesis is if this difference can be utilized to design communication schemes that opportunistically utilize the randomness, while giving some guarantees in performance for a worst case situation. The use of multiple transmit and receive antennas to deliver higher data rate at higher reliability, while transmitting over wireless channels, has been an extremely active research area over the past decade. The codes designed for such systems are referred to as space time codes. Diversity order, which captures reliability in terms of error performance, and rate impose a fundamental trade-off in space-time coding. High-rate space-time codes come at a cost of lower diversity order, and high reliability (diversity order) results in a lower rate. Over the past few years, this trade-off has been quite well understood for flat fading channels while far less attention has been given to Inter Symbol Interference (ISI) or broadband channels. Given the tradeoff between rate and reliability, if the overall system is designed for a fixed rate-diversity operating point it might be over-provisioning a resource which could be flexibly allocated to different applications. A new paradigm for the design of wireless links is proposed in this thesis which makes it possible to design a high rate code with an embedded high reliability code. This allows a form of communication where the high-rate code opportunistically takes advantage of good channel realizations whereas the embedded high-diversity code ensures that at least part of the information is received reliably. In this thesis the problem is studied from the point-of-view of information theoretic bounds on performance as well as explicit algebraic code designs for flat fading and ISI channels. Construction of a class of space-time codes which can flexibly allocate rate and reliability to an application is given. The constructions can be viewed as a generalization of classical multi-level codes to the fading multiple antenna channel. A systematic class of such codes is given using a construction which lifts rank properties of sets of binary matrix to the complex domain. These codes permit flexible allocation of rate and reliability for different streams. Diversity embedded codes for broadband (ISI) channels are developed by constructing maximal sets of Toeplitz binary matrices with rank guarantees. These constructions might be of independent interest in other distributed settings. From an information-theoretic point of view a channel is said to be successively refinable if it