Communications and signal processing

Summary

Wireless fidelity (WiFi) has been envisioned by the WiFi alliance as a single worldwide adopted standard for high-speed wireless local area networking. The term WiFi denotes wireless local area network (WLAN) technology based on IEEE 802.11 specifications. In this chapter, we provide an overview of the salient features and most important specifications of legacy and next-generation WLANs.

Legacy WLAN

WLANs based on IEEE 802.11 have become very popular in providing different data services. Figure 6.1 shows the general WLAN architecture, where an access point (AP) is connected to the Internet and/or other WLANs through a wired network infrastructure, referred to as the distribution system (DS). In this architecture, wireless stations (STAs) communicate with their associated AP using the medium access control (MAC) protocols defined in the IEEE 802.11 specifications.

Due to the use of unlicensed frequency bands (2.4 GHz with 14 distinct channels and 5 MHz) in IEEE 802.11b/g with data rates of up to 11/54 Mbps, WiFi networks have gained much attention (Kuran and Tugcu [2007]). During the last decade, various standards and/or amendments have been approved or initiated to enhance IEEE 802.11 based WiFi technology. Table 6.1 summarizes the IEEE 802.11 WiFi standard family.

The initial IEEE 802.11 physical (PHY) layer includes: (i) frequency hopping spread spectrum (FHSS), (ii) direct sequence spread spectrum (DSSS), and (iii) infrared (IR). IEEE 802.11b uses high-rate DSSS (HR-DSSS), while IEEE 802.11g deploys orthogonal frequency division multiplexing (OFDM). The IEEE 802.11 MAC layer deploys the distributed coordination function (DCF) as a default access technique.

Summary

The world has become heavily dependent on oil through the widespread use of combustion engines in gasoline cars, resulting in climate change, massive transfers of wealth to oil-producing countries, and heightened geopolitical tensions. The advent of commercially available electric vehicles (EVs) by the end of 2010 is expected to be a game changer that will shake things up in a fundamental manner. Not only can electricity be produced in a number of environmentally friendly ways, e.g., hydroelectric generators, wind farms, or solar arrays, but also the electric engine is significantly more efficient than the combustion engine of traditional gasoline cars or today's gasoline–electric hybrids (Davis [2010]). A promising example of using EVs for a sustainable electric mobility (e-mobility) in urban areas is the “e-mobility Berlin” project, which deploys only green electricity from renewable sources to realize a user-friendly public charging infrastructure for plug-in EVs (PEVs). The emission-free PEVs may be shared following DAIMLER's “car-to-go” idea and allow environmental zones to be set up in cities, from which environmentally friendly PEVs with no emissions are exempt (DAIMLER [2009]). Replacing gasoline vehicles with PEVs could reduce the importation of oil by up to 52% in the United States. Despite their huge potential to create new markets, revenues, and jobs, PEVs pose severe challenges to electric utility companies. A PEV being charged at home in the evening may more than double the average household electricity load and thereby dramatically exacerbates the load profile imbalance of power grids between off- and on-peak hours (Ipakchi and Albuyeh [2009]).

Summary

Radio-over-fiber (RoF) networks have been studied for many years as an approach to integrating optical fiber and wireless networks. In RoF networks, radio frequencies (RFs) are carried over optical fiber links between a central station and multiple low-cost remote antenna units (RAUs) in support of a variety of wireless applications. For instance, a distributed antenna system connected to the base station of a microcellular radio system via optical fibers was proposed in (Chu and Gans [1991]). To efficiently support time-varying traffic between the central station and its attached base stations, a centralized dynamic channel assignment method is applied at the central station of the proposed fiber optic microcellular radio system. To avoid having to equip each radio port in a fiber optic microcellular radio network with a laser and its associated circuit to control the laser parameters such as temperature, output power, and linearity, a cost-effective radio port architecture deploying remote modulation may be used (Wu et al. [1994]).

Apart from realizing low-cost microcellular radio networks, optical fibers can also be used to support a wide variety of other radio signals. RoF networks are attractive since they provide transparency against modulation techniques and are able to support various digital formats and wireless standards in a cost-effective manner. It was experimentally demonstrated in (Tang et al. [2004]) that RoF networks are well suited to simultaneously transmit wideband code division multiple access (WCDMA), IEEE 802.11a/g wireless local area network (WLAN), personal handyphone system (PHS), and global system for mobile communications (GSM) signals.

Summary

The network models we studied so far involve only one-way (feedforward) communication. Many communication systems are inherently interactive, allowing for cooperation through feedback and information exchange over multiway channels. In this chapter, we study the role of feedback in communication and present results on the two-way channel introduced by Shannon as the first multiuser channel. The role of multiway interaction in compression and secure communication will be studied in Chapters 20 and 22, respectively.

As we showed in Section 3.1.1, the capacity of a memoryless point-to-point channel does not increase when noiseless causal feedback is present. Feedback can still benefit point-to-point communication, however, by simplifying coding and improving reliability. The idea is to first send the message uncoded and then to use feedback to iteratively reduce the receiver's error about the message, the error about the error, and so on. We demonstrate this iterative refinement paradigm via the Schalkwijk–Kailath coding scheme for the Gaussian channel and the Horstein and block feedback coding schemes for the binary symmetric channel. We show that the probability of error for the Schalkwijk–Kailath scheme decays double-exponentially in the block length, which is significantly faster than the single-exponential decay of the probability of error without feedback.

We then show that feedback can enlarge the capacity region in multiuser channels. For the multiple access channel, feedback enlarges the capacity region by enabling statistical cooperation between the transmitters. We show that the capacity of the Gaussian MAC with feedback coincides with the outer bound obtained by allowing arbitrary (instead of product) joint input distributions. For the broadcast channel, feedback can enlarge the capacity region by enabling the sender to simultaneously refine both receivers’ knowledge about the messages. For the relay channel, we show that the cutset bound is achievable when noiseless causal feedback from the receiver to the relay is allowed. This is in contrast to the case without feedback in which the cutset bound is not achievable in general.

Finally, we discuss the two-way channel, where two nodes wish to exchange their messages interactively over a shared noisy channel. The capacity region of this channel is not known in general. We first establish simple inner and outer bounds on the capacity region.

Summary

We consider the problem of generating two descriptions of a source such that each description by itself can be used to reconstruct the source with some desired distortion and the two descriptions together can be used to reconstruct the source with a lower distortion. This problem is motivated by the need to efficiently communicate multimedia content over networks such as the Internet. Consider the following two scenarios:

Summary

We resume the discussion of broadcast channels started in Chapter 5. Again consider the 2-receiver DM-BCp(y1, y2|x) with private and common messages depicted in Figure 8.1. The definitions of a code, achievability, and capacity regions are the same as in Chapter 5. As mentioned before, the capacity region of the DM-BC is not known in general. In Chapter 5, we presented the superposition coding scheme and showed that it is optimal for several classes of channels in which one receiver is stronger than the other. In this chapter, we study coding schemes that can outperform superposition coding and present the tightest known inner and outer bounds on the capacity region of the general broadcast channel.

We first show that superposition coding is optimal for the 2-receiver DM-BC with degraded message sets, that is, when either R1 = 0 or R2 = 0. We then show that superposition coding is not optimal for BCs with more than two receivers. In particular, we establish the capacity region of the 3-receiver multilevel BC. The achievability proof involves the new idea of indirect decoding, whereby a receiver who wishes to recover only the common message still uses satellite codewords in decoding for the cloud center.

We then present Marton's inner bound on the private-message capacity region of the 2-receiver DM-BC and show that it is optimal for the class of semideterministic BCs. The coding scheme involves the multicoding technique introduced in Chapter 7 and the new idea of joint typicality codebook generation to construct dependent codewords for independent messages without the use of a superposition structure. The proof of the inner bound uses the mutual covering lemma, which is a generalization of the covering lemma in Section 3.7. Marton's coding scheme is then combined with superposition coding to establish an inner bound on the capacity region of the DM-BC that is tight for all classes of DM-BCs with known capacity regions. Next, we establish the Nair–El Gamal outer bound on the capacity region of the DM-BC. We show through an example that there is a gap between these inner and outer bounds. Finally, we discuss extensions of the aforementioned coding techniques to broadcast channels with more than two receivers and with arbitrary messaging requirements.

Summary

Confidentiality of information is a key consideration in many networking applications, including e-commerce, online banking, and intelligence operations. How can information be communicated reliably to the legitimate users, while keeping it secret from eavesdroppers? How does such a secrecy constraint on communication affect the limits on information flow in the network?

In this chapter, we study these questions under the information theoretic notion of secrecy, which requires each eavesdropper to obtain essentially no information about the messages sent from knowledge of its received sequence, the channel statistics, and the codebooks used. We investigate two approaches to achieve secure communication. The first is to exploit the statistics of the channel from the sender to the legitimate receivers and the eavesdroppers. We introduce the wiretap channel as a 2-receiver broadcast channel with a legitimate receiver and an eavesdropper, and establish its secrecy capacity, which is the highest achievable secret communication rate. The idea is to design the encoder so that the channel from the sender to the receiver becomes effectively stronger than the channel to the eavesdropper; hence the receiver can recover the message but the eavesdropper cannot. This wiretap coding scheme involves multicoding and randomized encoding.

If the channel from the sender to the receiver is weaker than that to the eavesdropper, however, secret communication at a positive rate is not possible. This brings us to the second approach to achieve secret communication, which is to use a secret key shared between the sender and the receiver but unknown to the eavesdropper. We show that the rate of such secret key must be at least as high as the rate of the confidential message. This raises the question of how the sender and the receiver can agree on such a long secret key in the first place. After all, if they had a confidential channel with sufficiently high capacity to communicate the key, then why not use it to communicate the message itself!

We show that if the sender and the receiver have access to correlated sources (e.g., through a satellite beaming common randomness to them), then they can still agree on a secret key even when the channel has zero secrecy capacity. We first consider the source model for key agreement, where the sender communicates with the receiver over a noiseless public broadcast channel to generate a secret key from their correlated sources.

Summary

In the first three parts of the book we investigated the limits on information flow in networks whose task is to communicate (or store) distributed information. In many real world distributed systems, such as multiprocessors, peer-to-peer networks, networked mobile agents, and sensor networks, the task of the network is to compute a function, make a decision, or coordinate an action based on distributed information. Can the communication rate needed to perform such a task at some node be reduced relative to communicating all the sources to this node?

This question has been formulated and studied in computer science under communication complexity and gossip algorithms, in control and optimization under distributed consensus, and in information theory under coding for computing and the μ -sum problem, among other topics. In this chapter, we study information theoretic models for distributed computing over networks. In some cases, we find that the total communication rate can be significantly reduced when the task of the network is to compute a function of the sources rather than to communicate the sources themselves, while in other cases, no such reduction is possible.

We first show that the Wyner–Ziv theorem in Chapter 11 extends naturally to the case when the decoder wishes to compute a function of the source and the side information. We provide a refined characterization of the lossless special case of this result in terms of conditional graph entropy. We then discuss distributed coding for computing. Although the rate–distortion region for this case is not known in general (even when the goal is to reconstruct the sources themselves), we show through examples that the total communication rate needed for computing can be significantly lower than for communicating the sources themselves. The first example we discuss is the μ -sum problem, where the decoder wishes to reconstruct a weighted sum of two separately encoded Gaussian sources with a prescribed quadratic distortion. We establish the rate–distortion region for this setting by reducing the problem to the CEO problem discussed in Chapter 12. The second example is lossless computing of the modulo-2 sum of a DSBS. Surprisingly, we find that using the same linear code at both encoders can outperform Slepian–Wolf coding.

Communications and signal processing

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Part II - Transform methods, bounds, and limits

6 - WiFi

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18 - Smart grid communications

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10 - RoF vs. R&F networks

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18 - DiscreteMemoryless Networks

17 - Interactive Channel Coding

Summary

1 - Introduction

13 - Multiple Description Coding

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Dedication

5 - Degraded Broadcast Channels

C - Cardinality Bounding Techniques

8 - General Broadcast Channels

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Part III - Multihop Networks

Acknowledgments

22 - Information Theoretic Secrecy

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2 - Information Measures and Typicality

7 - Channels with State

Contents

21 - Communication for Computing

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20 - Compression over Graphical Networks

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