Network information theory concerns the study of reliable communication in a network setting, where there are many sources and users who wish to communicate with each other. This field has recently attracted renewed attention due to fast-growing applications such as the Internet, wireless cellular and LAN data services, ad hoc networks and sensor networks. The wireless networks of the future allow the connectivity between many systems and users. Therefore it is of critical importance to study the interaction and behavior of interconnected systems: user interference, side information, robustness, security, user cooperation, etc.

Shannon’s information theory was a towering achievement of 20th century science and laid a theoretical foundation for understanding how to design optimal communication systems. Investigation on network information theory focuses on efficient and reliable communication in multi-terminal settings. The emphasis is on the information theoretic limits (channel coding) and compression (source coding) for simple network models, with the ultimate goal of understanding fundamental principles behind the information flow over more general networks. Topics include multiple access channels, broadcast channels, interference channels, relay channels, channels with state information, channels with feedback, two-way channels, Slepian-Wolf distributed data compression, source coding with side information, multiple descriptions; multiple-antenna (MIMO) Gaussian networks, asymptotic capacity of networks, network coding.

The fundamental limits of source-channel codes provide valuable insight into practical code design for networks. Recent advances in the area have received interest in codes for multiple antenna wireless channels (space-time codes), codes for multi-casting information (rateless codes), codes for efficient routing in cooperative communications (e.g. based on LDPC codes). This research aims to contribute to the creation of new ways of source and channel coding for noisy networks, and making existing coding techniques in presence of side information practical.

Channel and Source Coding with State Information

Most of multi-terminal scenarios are based on the idea of ‘‘decentralization of the state (or side) information’’. This idea comes from the well-known coding schemes of Wyner-Ziv and Gel’fand-Pinsker, which have been shown to be optimal for the single-user cases of source coding with state information at the decoder and channel coding with non-causal state information at the transmitter. Basically, these coding schemes enable one to make the optimal use of the state information to the non-relevant side, which results in lossless information rates. The optimality of such coding schemes for multi-terminal systems is still an unsolved problem. Furthermore, the information theoretic understanding of multi-terminal scenarios touches upon the basic theoretic models not yet fully understood, involving a number of challenging questions and unsolved problems. Some examples of these problems are : broadcast channels, multi-user channels with state information, coding for non-stationary and non-ergodic channels/sources with state information, joint coding and transmission of the state information, etc. The primary goal of this theoretical study is to understand the complex mechanisms of the state information into the different scenarios.

Partial Feedback and State Information, Mismatched Decoders

This investigation aims to explore the role of feedback in wireless communication networks and its relation to the resolution of the time-varying channel state. The main issues considered in this study is the effect of imperfect channel knowledge at the receiving end due to the time-varying nature of the wireless channel, and methods to encode it for the return channel as a function of the allocated bandwidth for feedback. Proper exploitation of incomplete (i.e. rate-limited and noisy) feedback for both point-to-point and multi-user problems (e.g. broadcast channels, multiple access channels, relay channels) will be investigated. Therefore, the performance limits of such scenarios depend heavily on the ability to track into the coding schemes the estimation errors of the parameters involved. Most of exciting results in multi-terminal systems may not hold or must be revised if only noisy estimates (perhaps very poor) of their statistics are available. On the other hand, the vast majority of literature in this area assumes matched decoding (that is the metrics or likelihoods used are based on the availability of the precise statistical characteristics of the channel). The investigation plans on attacking this aspect, and study the impact of metric mismatch on the rate performance of ergodic fading channels via the theory of large deviations. The joint effect of mismatched decoding and noisy feedback will be also studied.

Cooperative Communications in Wireless Networks

Network communications become more reliable and efficient when devices support each other to transmit data. Depending on the transmitter and receiver architectures and the information flow, there are many different configurations of networks. For example, the cooperative broadcast channels simply consists of a transmitter communicating information simultaneously to several receivers. Relay links are incorporated into the receivers to support user cooperation, so that the receivers are able to exchange their messages. The capacity regions of such scenarios have been only characterized in special cases. The reason for this is that optimal coding schemes are only known for the extremal positions of the relay nodes, i.e., when the relay is either very close to the transmitter (source node) or to the receiver (destination node). Whereas for the intermediate cases, optimal coding scheme remains unknown. Thus, the information theoretic analysis of such scenarios would provide powerful communication strategies for user cooperation in networks. The goal of this research consists in evaluating, in terms of capacity gain, the optimal trade-off between the benefits and limitations of cooperation in wireless communications, and including realistic constraints as delay and coordination requirements.

Network Coding for Wireless Networks

Various aspects related to coding at the physical layer in cooperative wireless networks will be addressed, aiming at providing better throughput, energy efficiency and resource utilization both in unicast and multi-cast communications. Unfortunately, globally optimal design of channel codes for general network environments is hard. Therefore it is necessary to consider other avenues in the pursuit of good practical codes for simple network models, with the ultimate goal of understanding the fundamental principles of general networks. In order to provide efficient solutions to this problem, the design of different channel codes will be explored, e.g. LDPC codes, rateless codes and distributed channel coding. One popular approach to perform network coding at relay nodes consists in decoding the messages from sources perfectly and then encoding to send it to the destination. However, this is a limiting factor in practical scenarios, i.e. in presence of deep fading conditions, where the relay nodes cannot fully decode the source messages. In order to avoid such limitation, novel codes with adaptive redundancy to the channel condition of the relay links are needed. This would enable to obtain network coding gains even when the relay nodes cannot perfectly decode the received messages. For example, a good strategy for each relay node might be to send the logarithm likelihood ratio (LLR) of the network coded message to the destination, which resembles to message passing in belief propagation algorithm.

Information-Theoretic Security for Wireless Networks

Most wireless systems today separate the problems of secure and reliable communication. Conventional cryptographic security is typically handled at the upper layers of the protocol stack, once the physical layer has been established and the communication between the friendly parties is error-free. However there exist theoretical results supporting the idea that extra security, and especially information theoretic (perfect) security, can be obtained by exploiting the physical layer. This fundamental notion of perfect secrecy was introduced by Shannon, who showed that the one-time pad was perfectly secure, i.e. an infinitely powerful attacker can extract precisely zero information from the encoded stream. Network coding opens the door to many interesting possibilities for information security. The use of multiple transmission paths may increase robustness to denial of service or jamming attacks. It can also provide security against eavesdroppers. This research explores some of the information-theoretic implications of security in multi-user systems and their advantages for wireless networks.