Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error probabilities for various problems are bounded above by a non-vanishing constant and the spotlight is shone on achievable coding rates as functions of the growing blocklengths. This represents the study of asymptotic estimates with non-vanishing error probabilities. In Part I, after reviewing the fundamentals of information theory, we discuss Strassen's seminal result for binary hypothesis testing where the type-I error probability is non-vanishing and the rate of decay of the type-II error probability with growing number of independent observations is characterized. In Part II, we use this basic hypothesis testing result to develop second- and sometimes, even third-order asymptotic expansions for point-to-point communication. Finally in Part III, we consider network information theory problems for which the second-order asymptotics are known. These problems include some classes of channels with random state, the multiple-encoder distributed lossless source coding (Slepian-Wolf) problem and special cases of the Gaussian interference and multiple-access channels. Finally, we discuss avenues for further research.Comment: Further comments welcom

Multiterminal Source-Channel Coding

Cooperative communication is seen as a key concept to achieve ultra-reliable communication in upcoming fifth-generation mobile networks (5G). A promising cooperative communication concept is multiterminal source-channel coding, which attracted recent attention in the research community. This thesis lays theoretical foundations for understanding the performance of multiterminal source-channel codes in a vast variety of cooperative communication networks. To this end, we decouple the multiterminal source-channel code into a multiterminal source code and multiple point-to-point channel codes. This way, we are able to adjust the multiterminal source code to any cooperative communication network without modification of the channel codes. We analyse the performance in terms of the outage probability in two steps: at first, we evaluate the instantaneous performance of the multiterminal source-channel codes for fixed channel realizations; and secondly, we average the instantaneous performance over the fading process. Based on the performance analysis, we evaluate the performance of multiterminal source-channel codes in three cooperative communication networks, namely relay, wireless sensor, and multi-connectivity networks. For all three networks, we identify the corresponding multiterminal source code and analyse its performance by the rate region for binary memoryless sources. Based on the rate region, we derive the outage probability for additive white Gaussian noise channels with quasi-static Rayleigh fading. We find results for the exact outage probability in integral form and closed-form solutions for the asymptotic outage probability at high signal-to-noise ratio. The importance of our results is fourfold: (i) we give the ultimate performance limits of the cooperative communication networks under investigation; (ii) the optimality of practical schemes can be evaluated with respect to our results, (iii) our results are suitable for link-level abstraction which reduces complexity in network-level simulation; and (iv) our results demonstrate that all three cooperative communication networks are key technologies to enable 5G applications, such as device to device and machine to machine communications, internet of things, and internet of vehicles. In addition, we evaluate the performance improvement of multiterminal source-channel codes over other (non-)cooperative communications concepts in terms of the transmit power reduction given a certain outage probability level. Moreover, we compare our theoretical results to simulated frame-error-rates of practical coding schemes. Our results manifest the superiority of multiterminal source-channel codes over other (non-)cooperative communications concepts

Side information aware source and channel coding in wireless networks

Signals in communication networks exhibit significant correlation, which can stem from the physical nature of the underlying sources, or can be created within the system. Current layered network architectures, in which, based on Shannon’s separation theorem, data is compressed and transmitted over independent bit-pipes, are in general not able to exploit such correlation efficiently. Moreover, this strictly layered architecture was developed for wired networks and ignore the broadcast and highly dynamic nature of the wireless medium, creating a bottleneck in the wireless network design. Technologies that exploit correlated information and go beyond the layered network architecture can become a key feature of future wireless networks, as information theory promises significant gains. In this thesis, we study from an information theoretic perspective, three distinct, yet fundamental, problems involving the availability of correlated information in wireless networks and develop novel communication techniques to exploit it efficiently. We first look at two joint source-channel coding problems involving the lossy transmission of Gaussian sources in a multi-terminal and a time-varying setting in which correlated side information is present in the network. In these two problems, the optimality of Shannon’s separation breaks down and separate source and channel coding is shown to perform poorly compared to the proposed joint source-channel coding designs, which are shown to achieve the optimal performance in some setups. Then, we characterize the capacity of a class of orthogonal relay channels in the presence of channel side information at the destination, and show that joint decoding and compression of the received signal at the relay is required to optimally exploit the available side information. Our results in these three different scenarios emphasize the benefits of exploiting correlated side information at the destination when designing a communication system, even though the nature of the side information and the performance measure in the three scenarios are quite different.Open Acces

Channel Access in Wireless Networks: Protocol Design of Energy-Aware Schemes for the IoT and Analysis of Existing Technologies

The design of channel access policies has been an object of study since the deployment of the first wireless networks, as the Medium Access Control (MAC) layer is responsible for coordinating transmissions to a shared channel and plays a key role in the network performance. While the original target was the system throughput, over the years the focus switched to communication latency, Quality of Service (QoS) guarantees, energy consumption, spectrum efficiency, and any combination of such goals. The basic mechanisms to use a shared channel, such as ALOHA, TDMA- and FDMA-based policies, have been introduced decades ago. Nonetheless, the continuous evolution of wireless networks and the emergence of new communication paradigms demand the development of new strategies to adapt and optimize the standard approaches so as to satisfy the requirements of applications and devices. This thesis proposes several channel access schemes for novel wireless technologies, in particular Internet of Things (IoT) networks, the Long-Term Evolution (LTE) cellular standard, and mmWave communication with the IEEE802.11ad standard. The first part of the thesis concerns energy-aware channel access policies for IoT networks, which typically include several battery-powered sensors. In scenarios with energy restrictions, traditional protocols that do not consider the energy consumption may lead to the premature death of the network and unreliable performance expectations. The proposed schemes show the importance of accurately characterizing all the sources of energy consumption (and inflow, in the case of energy harvesting), which need to be included in the protocol design. In particular, the schemes presented in this thesis exploit data processing and compression techniques to trade off QoS for lifetime. We investigate contention-free and contention-based chanel access policies for different scenarios and application requirements. While the energy-aware schemes proposed for IoT networks are based on a clean-slate approach that is agnostic of the communication technology used, the second part of the thesis is focused on the LTE and IEEE802.11ad standards. As regards LTE, the study proposed in this thesis shows how to use machine-learning techniques to infer the collision multiplicity in the channel access phase, information that can be used to understand when the network is congested and improve the contention resolution mechanism. This is especially useful for massive access scenarios; in the last years, in fact, the research community has been investigating on the use of LTE for Machine-Type Communication (MTC). As regards the standard IEEE802.11ad, instead, it provides a hybrid MAC layer with contention-based and contention-free scheduled allocations, and a dynamic channel time allocation mechanism built on top of such schedule. Although this hybrid scheme is expected to meet heterogeneous requirements, it is still not clear how to develop a schedule based on the various traffic flows and their demands. A mathematical model is necessary to understand the performance and limits of the possible types of allocations and guide the scheduling process. In this thesis, we propose a model for the contention-based access periods which is aware of the interleaving of the available channel time with contention-free allocations

Joint Source-Channel Codes for MIMO Block Fading Channels

We consider transmission of a continuous amplitude source over an L-block Rayleigh fading $M_t \times M_r$ MIMO channel when the channel state information is only available at the receiver. Since the channel is not ergodic, Shannon's source-channel separation theorem becomes obsolete and the optimal performance requires a joint source -channel approach. Our goal is to minimize the expected end-to-end distortion, particularly in the high SNR regime. The figure of merit is the distortion exponent, defined as the exponential decay rate of the expected distortion with increasing SNR. We provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths. For the lower bounds, we analyze three different strategies based on layered source coding concatenated with progressive, superposition or hybrid digital/analog transmission. In each case, by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio. We prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom, that is L=1, and $\min\{M_t,M_r\}=1$. When we have more degrees of freedom, our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio. We demonstrate that our results, which were derived for a complex Gaussian source, can be extended to more general source distributions as well.Comment: 36 pages, 11 figure