MULTI-USER INFORMATION THEORY: STATE INFORMATION AND IMPERFECT CHANNEL KNOWLEDGE

The capacity of single and multi-user state-dependent channels under imperfect channel knowledge at the receiver(s) and/or transmitter are investigated. We address these channel mismatch scenarios by introducing two novel notions of reliable communication under channel estimation errors, for which we provide an associated coding theorem and its corresponding converse, assuming discrete memoryless channels. Basically, we exploit for our purpose an interesting feature of channel estimation through use of pilot symbols. This feature is the availability of the statistic characterizing the quality of channel estimates. In this thesis we first introduce the notion of estimation-induced outage capacity for single-user channels, where the transmitter and the receiver strive to construct codes for ensuring reliable communication with a quality of service (QoS), no matter which degree of accuracy estimation arises during a transmission. In our setting, the quality of service constraint stands for achieving target rates with small error probability (the desired communication service), even for very poor channel estimates. Our results provide intuitive insights on the impact of the channel estimates and the channel characteristics (e.g. SNR, number of pilots, feedback rate) on the maximal mean outage rate. Then the optimal decoder achieving this capacity is investigated. We focus on the family of decoders that can be implemented on most practical coded modulation systems. Based on the theoretical decoder that achieves the capacity, we derive a practical decoding metric for arbitrary memoryless channels that minimizes the average of the transmission error probability over all channel estimation errors. Next, we specialize this metric for the case of fading MIMO channels. According to our notion of outage rates, we characterize maximal achievable information rates of the proposed decoder using Gaussian codebooks. Numerical results show that the derived metric provides significant gains, in terms of achievable information rates and bit error rate (BER), in a bit interleaved coded modulation (BICM) framework, without introducing any additional decoding complexity. We next consider the effects of imperfect channel estimation at the receivers with imperfect (or without) channel knowledge at the transmitter on the capacity of state-dependent channels with non-causal channel state information at the transmitter. We address this through the notion of reliable communication based on the average of the transmission error probability over all channel estimation errors. This notion allows us to consider the capacity of a composite (more noisy) Gelfand and Pinsker's channel. We derive the optimal Dirty-paper coding (DPC) scheme that achieves the capacity (assuming Gaussian inputs) of the fading Costa channel under the mentioned conditions. The results illustrate a practical trade-off between the amount of training and its impact to the interference cancellation performances of DPC scheme. This approach enable us to study the capacity region of the multiuser Fading MIMO Broadcast Channel (MIMO-BC), where the mobiles (the receivers) only dispose of a noisy estimate of the channel parameters, and these estimates may be (or not) available at the base station (the transmitter). In particular, we observe the surprising result that a BC with a single transmitter and receiver antenna, and imperfect channel estimation at each receiver, does not need the knowledge of estimates at the transmitter to achieve large rates. Finally, we consider several implementable DPC schemes for multi-user information embedding, through emphasizing their tight relationship with conventional multi-user information theory. We first show that depending on the targeted application and on whether the different messages are asked to have different robustness and transparency requirements, multi-user information embedding parallels the Gaussian BC and the Gaussian Multiple Access Channel (MAC) with non-causal channel state information at the transmitter(s). Based on the theoretical DPC, we propose practical coding schemes for these scenarios. Our results extend the practical implementations of QIM, DC-QIM and SCS from the single user case to the multi-user one. Then, we show that the gap to full performance can be bridged up using finite dimensional lattice codebooks.