Multiple user information theory

A unified framework is given for multiple user information networks. These networks consist of several users communicating to one another in the presence of arbitrary interference and noise. The presence of many senders necessitates a tradeoff in the achievable information transmission rates. The goal is the characterization of the capacity region consisting of all achievable rates. The focus is on broadcast, multiple access, relay, and other channels for which the recent theory is relativdy well developed. A discussion of the Gaussian version of these channels demonstrates the concreteness of the encoding and decoding necessary to achieve optimal information flow. We also offer speculations about the form of a general theory of information flow in networks.     

Interference Channels With Common Information

In this paper, the interference channel with common information (ICC), in which two senders need deliver not only private messages but also certain common messages to their corresponding receivers, is investigated. An achievable rate region for such a channel is obtained by applying a superposition coding scheme that consists of successive encoding and simultaneous decoding. It is shown that the derived achievable rate region includes or extends several existing results for the interference channels with or without common information. The rate region is then specialized to a class of ICCs in which one sender has no private information to transmit, and a class of deterministic interference channels with common information (DICCs). In particular, the derived rate region is found to be the capacity region for this class of DICCs. Last, the achievable rate region derived for the discrete memoryless ICC is extended to the Gaussian case, in which a numerical example is provided to illustrate the improvement of our rate region over an existing result.     

On the Achievable Rates of Multiband Ultra-Wideband Systems

In this work we study the achievable rates of memoryless signaling strategies adapted to ultra-wideband (UWB) multipath fading channels. We focus on strategies that do not have explicit knowledge of the instentaneous channel realization, but may have knowledge of the channel statistics. We evaluate the average mutual information of the general binary flash-signaling rates as a function of channel statistics and derive random coding bounds for m-ary PPM using different noncoherent receivers as well as an imperfect coherent receiver. Then we extend the results to multiband m-PPM signaling and show that for data rates on the order of 400 Mbits/s, at 4 m distance between the transmitter and the receiver, can be achieved using simple noncoherent receivers.     

Suboptimality of TDMA in the low-power regime

We consider multiaccess, broadcast, and interference channels with additive Gaussian noise. Although the set of rate pairs achievable by time-division multiple access (TDMA) is not equal to the capacity region, the TDMA achievable region converges to the capacity region as the power decreases. Furthermore, TDMA achieves the optimum minimum energy per bit. Despite those features, this paper shows that the growth of TDMA-achievable rates with the energy per bit is suboptimal in the low-power regime except in special cases: multiaccess channels where the users' energy per bit are identical and broadcast channels where the receivers have identical signal-to-noise ratios. For the additive Gaussian noise interference channel, we identify a small region of interference parameters outside of which TDMA is also shown to be suboptimal. The effect of fading (known to the receiver) on the suboptimality of TDMA is also explored.     

On Information Rates of Time-Varying Fading Channels Modeled as Finite-State Markov Channels

We study information rates of time-varying flatfading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR ≲12 dB) and at medium to fast normalized fading rates (0.01 ≲fDT ≲0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT ≲0.01.     

Achievable information rates and coding for MIMO systems over ISI channels and frequency-selective fading channels

We propose a simulation-based method to compute the achievable information rates for general multiple-input multiple-output (MIMO) intersymbol interference (ISI) channels with inputs chosen from a finite alphabet. This method is applicable to both deterministic and stochastic channels. As an example of the stochastic MIMO ISI channels, we consider the multiantenna systems over frequency-selective fading channels, and quantify the improvement in the achievable information rates provided by the additional frequency diversity (for both ergodic and nonergodic cases). In addition, we consider the multiaccess multiantenna system and present some results on the achievable information-rate region. As for the deterministic MIMO ISI channels, we use the binary-input multitrack magnetic recording system as an example, which employs multiple write and read heads for data storage. Our results show that the multitrack recording channels have significant advantages over the single-track channels, in terms of the achievable information rates when the intertrack interference is considered. We further consider practical coding schemes over both stochastic and deterministic MIMO ISI channels, and compare their performance with the information-theoretical limits. Specifically, we demonstrate that the performance of the turbo coding/decoding scheme is only about 1.0 dB away from the information-theoretical limits at a bit-error rate of 10/sup -5/ for large interleaver lengths.     

On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.     

Capacity Theorems for the “Z” Channel

We consider the two-user "Z" channel (ZC), where there are two senders and two receivers. One of the senders transmits information to its intended receiver (without interfering with the unintended receiver), while the other sender transmits information to both receivers. The complete characterization of the discrete memoryless ZC remains unknown to date. For the Gaussian ZC, the capacity has only been established for a crossover link gain of 1. In this work, we study both the discrete memoryless ZC and the Gaussian ZC. We first establish achievable rates for the general discrete memoryless ZC. The coding strategy uses rate-splitting and superposition coding at the sender with information for both receivers. At the receivers, we use joint decoding. We then specialize the rates obtained to two different types of degraded discrete memoryless ZCs and also derive respective outer bounds to their capacity regions. We show that as long as a certain condition is satisfied, the achievable rate region is the capacity region for one type of degraded discrete memoryless ZC. The results are then extended to the two-user Gaussian ZC with different crossover link gains. We determine an outer bound to the capacity region of the Gaussian ZC with strong crossover link gain and establish the capacity region for moderately strong crossover link gain     

Carbon Copying Onto Dirty Paper

A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference (in addition to the additive noise), which is known noncausally to the transmitter but not to any of the receivers. Applications range from wireless multiple-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and binary special cases. In most cases, we observe that the availability of side information at the transmitter increases capacity relative to systems without such side information, and that the lack of side information at the receivers decreases capacity relative to systems with such side information. For the noiseless binary case, we establish the capacity when there are two receivers. When there are many receivers, we show that the transmitter side information provides a vanishingly small benefit. When the interference is large and independent across the users, we show that time sharing is optimal. For the Gaussian case, we present a coding scheme and establish its optimality in the high signal-to-interference-plus-noise limit when there are two receivers. When the interference power is large and independent across all the receivers, we show that time-sharing is again optimal. Connections to the problem of robust dirty paper coding are also discussed     

The implementation of channel diversity in mobile software radio receivers

A novel channel diversity concept is proposed and demonstrated, which avoids receiving signal deterioration due to multipath fading in mobile receivers. The system is based on coherent superposition of the signals received from several transmitters supplying the same information at different frequencies. Based on a software radio architecture this concept may increase the quality of mobile reception in modern car receivers considerably. Compared with multiantenna-receivers which overcome the multipath fading problem by simultaneously receiving the same program with several antennas, the proposed solution is advantageous, since it requires only a single antenna.     

Secure Broadcasting Over Fading Channels

We study a problem of broadcasting confidential messages to multiple receivers under an information-theoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are considered: parallel channels and fast-fading channels. For the case of reversely degraded parallel channels, one eavesdropper, and an arbitrary number of legitimate receivers, we determine the secrecy capacity for transmitting a common message, and the secrecy sum-capacity for transmitting independent messages. For the case of fast-fading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while that of the eavesdropper is known only to itself. We show that, using a suitable binning strategy, a common message can be reliably and securely transmitted at a rate independent of the number of receivers. We also show that a simple opportunistic transmission strategy is optimal for the reliable and secure transmission of independent messages in the limit of large number of receivers.     

Capacity Bounds for Broadcast Channels With Confidential Messages

This paper studies capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. Both inner and outer bounds are proposed to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csiszar and Korner's rate equivocation region for broadcast channels with a single confidential message, Liu 's achievable rate region for broadcast channels with perfect secrecy, Marton's and Gel'fand-Pinsker's achievable rate region for general broadcast channels. The proposed outer bounds, together with the inner bound, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages, including the less noisy, deterministic, and semideterministic broadcast channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, the proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.     

On the Achievable Rate for Wideband Channels with Estimated CSI

We consider the achievable rate for frequency-selective fading channels when the channel state information (CSI) is to be estimated at the receiver. Since the estimated CSI is not perfect, the achievable rate must be degraded from that with perfect CSI. Using the rate-distortion theory, we study an upper bound on the achievable rate and investigate how the achievable rate can be maximized through an optimization problem by allocating the resources such as degrees of freedom (the transmission time in our work or transmission power) for the exploration of CSI (i.e., the channel estimation) using pilot symbols, and the exploitation of channels to transmit data symbols. Although our study is based on some ideal assumptions, the results could help develop flexible communication systems such as software defined radio (SDR) to achieve a best performance by optimizing radio resources for unknown channels.     

On Reliable Communications over Channels Impaired by Bursty Impulse Noise

Digital communications over channels impaired by impulse noise are addressed. We adopt a two-state Markov model that allows to describe the typical bursty nature of the impulse noise, in contrast to the memoryless models generally considered in the literature. For this channel, we evaluate the achievable information rate and propose a couple of practical communication systems based on powerful codes and iterative receivers. Moreover, we discuss the effectiveness of the considered receivers in terms of performance/latency tradeoff as well as in terms of robustness to erroneous channel estimations. The proposed schemes are shown to perform fairly close to the theoretical limits, and significantly better than the conventional schemes employing memoryless detection.     

Discrete Memoryless Interference and Broadcast Channels With Confidential Messages: Secrecy Rate Regions

We study information-theoretic security for discrete memoryless interference and broadcast channels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers while ensuring mutual information-theoretic secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. In this paper, we present inner and outer bounds on secrecy capacity regions for these two communication systems. The derived outer bounds have an identical mutual information expression that applies to both channel models. The difference is in the input distributions over which the expression is optimized. The inner bound rate regions are achieved by random binning techniques. For the broadcast channel, a double-binning coding scheme allows for both joint encoding and preserving of confidentiality. Furthermore, we show that, for a special case of the interference channel, referred to as the switch channel, derived bounds meet. Finally, we describe several transmission schemes for Gaussian interference channels and derive their achievable rate regions while ensuring mutual information-theoretic secrecy. An encoding scheme in which transmitters dedicate some of their power to create artificial noise is proposed and shown to outperform both time-sharing and simple multiplexed transmission of the confidential messages.     

Distributed MIMO Systems for Nomadic Applications Over a Symmetric Interference Channel

A single source communicates with a single destination via a remote wireless multiple-antenna (multiple-input multiple-output (MIMO)) transceiver. The source has access to each of the transmit antennas through a finite-capacity link, and likewise the destination is connected to the receiving antennas via capacity-constrained channels (e.g., as for wired or time-division multiple access (TDMA) channels). Targeting a nomadic communication scenario, in which the remote MIMO transceiver is designed to serve different standards or services, it is assumed that transmitters and receivers are oblivious to the encoding function shared by source and destination. Assuming a Gaussian symmetric interference network as the channel model (as for regularly placed transmitters and receivers), achievable rates are investigated and compared with an upper bound (that holds also for codebook-dependent operation). Closed-form expressions are derived for large numbers of antennas (and in some cases large signal-to-noise ratios (SNRs)), and asymptotics of the achievable rates are studied with respect to either link capacities or SNR. Overall, the analysis points to effective transmission/reception strategies for the distributed MIMO channel at hand, which are optimal under specified conditions. In particular, it is concluded that in certain asymptotic and nonasymptotic regimes there is no loss of optimality in designing the system for nomadic applications (i.e., assuming oblivious transmitters and receivers). Numerical results validate the analysis.      

Random coding theorems for the general discrete memoryless broadcast channel

Three different communication situations are considered for the general nondegraded discrete memoryless broadcast channel with two components. In the most general situation, common and separate information is sent to both receivers. In another situation, only separate information is sent, and in a third, one Common and one separate message is sent. For each communication situation a random coding inner bound on the capacity region is derived. An example is presented which Shows that in the most general situation the inner bound strictly dominates the family of rates obtained by time-sharing. The capacity region for the general situation is characterized by a limiting expression. The relationship with the degraded broadcast channel and the connection with other multiway channels, such as the channel with two senders and two receivers, is shown.     

Scalable reliable multicast using multiple multicast channels

We examine an approach for providing reliable, scalable multicast communication, involving the use of multiple multicast channels for reducing receiver processing costs and reducing network bandwidth consumption in a multicast session. In this approach a single multicast channel is used for the original transmission of packets. Retransmissions of packets are done on separate multicast channels, which receivers dynamically join and leave. We first show that protocols using an infinite number of multicast channels incur much less processing overhead at the receivers compared to protocols that use only a single multicast channel. This is due to the fact that receivers do not receive retransmissions of packets they have already received correctly. Next, we derive the number of unwanted redundant packets at a receiver due to using only a finite number of multicast channels, for a specific negative acknowledgment (NAK)-based protocol. We then explore the minimum number of multicast channels required to keep the cost of processing unwanted packets to a sufficiently low value. For an application consisting of a single sender transmitting reliably to many receivers we find that only a small number of multicast channels are required for a wide range of system parameters. In the case of an application where all participants simultaneously act as both senders and receivers a moderate number of multicast channels is needed. Finally, we present two mechanisms for implementing multiple multicast channels, one using multiple IP multicast groups and the other using additional router support for selective packet forwarding. We discuss the impact of both mechanisms on performance in terms of end-host and network resources     

Transmission scheduling in a multi‐channel wireless network with bidirectional relaying links

Using network coding in a wireless network can potentially improve the network throughput. On the other hand, it increases the complexity of resource allocations as the quality of one transmission is affected by the link conditions of the transmitter to multiple receivers. In this work, we study time slot scheduling and channel allocations jointly for a network with bidirectional relaying links, where the two end nodes of each link can exchange data through a relay node. Two scenarios are considered when the relay node forwards packets to the end nodes. In the first scenario, the relay node always forwards network‐coded packets to both end nodes simultaneously; in the second scenario, the relay node opportunistically uses network coding for two‐way relaying and traditional one‐way relaying. For each scenario, an optimization problem is first formulated for maximizing the total network throughput. The optimum scheduling is not causal because it requires future information of channel conditions. We then propose heuristic scheduling schemes. The slot‐based scheduling maximizes the total transmission rate of all the nodes at each time slot, and the node‐based scheduling schedules transmissions based on achievable transmission rates of individual nodes at different channels. The node‐based one has lower complexity than the slot‐based one. Our results indicate that although the node‐based scheduling achieves slightly lower throughput than the slot‐based one, both the proposed scheduling schemes are very effective in the sense that the difference between their throughput and the optimum scheduling is relatively small in different network settings. Copyright © 2015 John Wiley & Sons, Ltd.