The initial focus of this chapter is on the most significant issue to solve in the MAC sublayer of LANs and MANs: how to allow a given number of stations to share a common channel to communicate. Among the different solutions that can be devised, the answer successfully adopted by current LANs is introduced and critically commented on.

Such treatment is followed by a description of the general IEEE framework where LAN and MAN standards sit. There finds its place the standard for the implementation of Ethernet LANs, also known as the IEEE 802.3 standard, whose physical layer and MAC sublayer specifications are faced next. An adequate coverage is provided for the admissible topologies, MAC frame format and main algorithms; the evolution that this type of LAN has undergone in the last years is also illustrated, from the original solutions to fast and current gigabit Ethernet networks.

What follows is a description of the reference standards that modern cabling systems have to conform to. The intent is twofold: to make the reader understand (i) how crucial the cabling system is in guaranteeing a successfully operative network; (ii) how important its physical properties are when striving to support higher and higher data rates.

The chapter is closed by a few dense practices, which aim at explaining several real-world issues: the relation between layer-3 and layer-2 addressing schemes; the configuration of the hardware device that allows the station to connect to the LAN and to the Internet; and the layout of the cabling system for a campus network.

This chapter takes the reader into the modern world of computer networks: it first illustrates the main standardization bodies for telecommunications and data networking, then it exposes the general principles that underlie communications in a packet-switched network and describes the features of the main protocols ruling the proper functioning of the Internet.

An adequate, thorough treatment is devoted to the Internet protocol (IP), as its functionalities are the basis on which the entire Internet communication model relies: the original classful and the current classless addressing schemes are presented, followed by the subnetting and supernetting procedures IP allows. Direct and indirect datagram delivery is also introduced. Every topic is complemented by some explanatory examples, whose aim is immediately to translate into useful, working cases, the theoretical concepts.

The chapter is closed by two sections that present the salient attributes of the transmission control protocol (TCP) and of the user datagram protocol (UDP).

Who's who in the telecommunication world

It is appropriate to place in this opening section a brief, yet meaningful overview of the most representative bodies within the telecommunication and networking arena, and of their role. As the topics covered in the next chapters will quantitatively testify, the networking field heavily relies upon standards: they are needed to guarantee for systems and services not only quality, safety, reliability and efficiency, but also interoperability, a magic word when the ultimate objective is to “connect.”

In the previous chapters the most popular solutions for wired and wireless local area networks have been presented. Signal propagation impairments, on one side, and the multiple access technique adopted by the MAC, on the other, contribute to limit both the maximum distance that a LAN is capable of covering and its achievable performance.

However, the need to deploy LANs spanning larger areas, like an entire enterprise or university campus, has pushed toward the implementation of specific devices that allow these limits to be circumvented: repeaters, bridges and switches [65]. Such devices are also used to implement high-performance and flexible cabling schemes, according to the most up-to-date standard requirements.

This chapter describes these commonly used LAN devices, and then discusses a widely accepted solution for traffic isolation using virtual LANs. The chapter ends with a few practical examples of LAN device management and virtual LAN configuration.

Repeaters and bridges

It has already been mentioned that signal quality degrades with distance, so that a maximum span exists, beyond which a receiver cannot correctly recover the associated information.

This constraint can be bypassed using a repeater, an active device that links two or more LAN segments, with the goal of extending the physical connection between two LAN stations. A repeater amplifies a signal received on any input port and repeats it to all output ports. A repeater decodes incoming bit streams, re-encodes and resynchro-nizes them before retransmission. A repeater can then be classified as a layer-1 device. Regarding the synchronism regeneration, a repeater achieves it either by buffering part of the frame and then adding a delay, or by cutting some header bits for the time required to get resynchronized.

Finite geometries, such as Euclidean and projective geometries, are powerful mathematical tools for constructing error-control codes. In the 1960s and 1970s, finite geometries were successfully used to construct many classes of easily implementable majority-logic decodable codes. In 2000, Kou, Lin, and Fossorier [1–3] showed that finite geometries can also be used to construct LDPC codes that perform well and close to the Shannon theoretical limit with iterative decoding based on belief propagation. These codes are called finite-geometry (FG)-LDPC codes. FG-LDPC codes form the first class of LDPC codes that are constructed algebraically. Since 2000, there have been many major developments in construction of LDPC codes based on various structural properties of finite geometries [4–18]. In this chapter, we put together all the major constructions of LDPC codes based on finite geometries under a unified frame. We begin with code constructions based on Euclidean geometries and then go on to discuss those based on projective geometries.

Construction of LDPC Codes Based on Lines of Euclidean Geometries

This section presents a class of cyclic LDPC codes and a class of quasi-cyclic (QC) LDPC codes constructed using lines of Euclidean geometries. Before we present the constructions of these two classes of Euclidean-geometry (EG)-LDPC codes, we recall some fundamental structural properties of a Euclidean geometry that have been discussed in Chapter 2.

In the previous chapters, a few network devices have been presented. Repeaters are layer-1 devices that perform functions related to physical signal processing. Bridges are layer-2 devices that are able to detect frames and interpret their fields, such as MAC addresses. A switch is a multiport bridge, still a layer-2 device, but with high frame-processing performance.

Even if LAN interconnections in wide areas may be done by using bridges, and until the early 1990s this was quite common, the best way for managing wide area connections is through layer-3 devices, usually called routers. Routers perform all functions from layer-1 up to layer-3: they can process packets and are the main devices for network layer management. Indeed, routers represent the most important intermediate systems used to interconnect heterogeneous networks on a geographical scale, building a consistent and cooperative complex system commonly known as an internet.

This chapter illustrates the main concepts behind IP-based routers, discussing the most important functions performed and describing the most common architectures available. Some details of the IP packet processing and forwarding operations are provided, followed by the description of more advanced network layer functionalities, such as packet filtering and address translation. The chapter is concluded by a few practical configuration examples.

What is a router?

A possible way to start presenting routers is to try to compare them with bridges [65]. A bridge physically connects different LANs but, actually, they can be logically considered the same network, with the same network rules and the same network protocol. A router, on the other hand, completely separates LANs and networks, both physically and logically.

Low-density parity-check (LDPC) codes are a class of linear block codes with implementable decoders, which provide near-capacity performance on a large set of data-transmission and data-storage channels. LDPC codes were invented by Gallager in his 1960 doctoral dissertation and were mostly ignored during the 35 years that followed. One notable exception is the important work of Tanner in 1981, in which Tanner generalized LDPC codes and introduced a graphical representation of LDPC codes, now called a Tanner graph. The study of LDPC codes was resurrected in the mid 1990s with the work of MacKay, Luby, and others [3–6], who noticed, apparently independently of Gallager's work, the advantages of linear block codes with sparse (low-density) parity-check matrices.

This chapter introduces LDPC codes and creates a foundation for further study of LDPC codes in later chapters. We start with the fundamental representations of LDPC codes via parity-check matrices and Tanner graphs. We then learn about the decoding advantages of linear codes that possess sparse parity-check matrices. We will see that this sparseness characteristic makes the code amenable to various iterative decoding algorithms, which in many instances provide near optimal performance. Gallager of course recognized the decoding advantages of such low-density parity-check codes and he proposed a decoding algorithm for the BI-AWGNC and a few others for the BSC. These algorithms have received much scrutiny in the past decade, and are still being studied.

The intent of this chapter is to complement the previous discussion on wired LANs, providing a thorough picture of the technologies and standards available today to build wireless network infrastructures. These aim to cover a wide range of areas successfully, spanning from personal to local and metropolitan coverage solutions.

The impressive pace of technological advances of the last decade has acquainted us with technologies that replace cable over very short distances, as testified by palm computers, cellular headsets and plenty of technological “toys” equipped with Bluetooth ports. Wireless LANs have an unprecedented popularity too, rapidly pervading private houses and enterprises; in metropolitan areas, municipalities are also getting into the game, supporting projects of wireless connectivity for communities that would otherwise be confined to low-speed Internet access. This all started with some impressive – at the time – 1 and 2 Mbit/s raw transmission rates that the first Wireless LAN standard guaranteed: current products achieve 54 Mbit/s of raw throughput, rates of 250 Mbit/s are on the way, and the specifications for wireless MAN head to even higher data rates, extended coverage and mobility support.

The logical organization of the chapter reflects the colloquial description above: the first section is devoted to wireless LANs and to the corresponding set of specifications, belonging to the IEEE 802.11 family of standards; the second section deals with the issue of fixed – and mobile – radio broadband access that wireless MANs have to provide. For the sake of completeness, the next sections rapidly look at wireless personal area networks (WPANs) and wireless mesh networks. The chapter is closed by some practical – and crucial – considerations on traffic monitoring and security issues in wireless networks.

In this chapter we cover some of the more common applications of LDPC codes. The breadth and depth of work reported in the literature on the application of LDPC codes to data transmission and storage would fill many volumes. Thus, this chapter has the modest goal of introducing selected applications. These applications include coded modulation, turbo equalization and code design for intersymbol-interference channels, estimation of the level LDPC error floors, and decoder design for low error floors. We also provide in this chapter a brief introduction to LDPC convolutional codes. Because of their importance, we also include a section on so-called digital fountain codes, which have application to file transfer over networks and closely resemble LDPC codes.

LDPC-Coded Modulation

Trellis-coded modulation, multilevel coding, and bit-interleaved coded modulation (BICM), are all well-known bandwidth- and power-efficient coded-modulation schemes. More recently, turbo and LDPC codes have been combined with higher-order modulation schemes. For example, LDPC codes have been designed for multilevel coding in [6] and for MIMO channels in [7]. Near-capacity performance has been demonstrated in these higher-order signaling systems. The system under study is shown in Figure 15.1. We do not consider the multilevel coding format because it is shown in [8] and elsewhere that the single-code format of Figure 15.1 is superior for LDPC codes. Although this is a BICM-like system, because an LDPC encoder is employed, a bit interleaver is not necessary here. An interleaver would be equivalent to permuting the columns in the code's parity-check matrix.

Turbo codes, which were first presented to the coding community in 1993, represent one of the most important breakthroughs in coding since Ungerboeck introduced trellis codes in 1982. In fact, the invention of turbo codes and their iterative “turbo” decoders started a revolution in iteratively decodable codes and iterative receiver processing (such as “turbo equalization”). Most frequently, a turbo code refers to a concatenation of two (or more) convolutional encoders separated by interleavers. The turbo decoder consists of two (or more) soft-in/soft-out convolutional decoders which iteratively feed probabilistic information back and forth to each other in a manner that is reminiscent of a turbo engine. In this chapter we introduce the most important classes of turbo codes, provide some heuristic justification as to why they should perform well, and present their iterative decoders. Our focus will be on parallel-and serial-concatenated convolutional codes (PCCCs and SCCCs) on the binary-input AWGN channel, but we also include the important class of turbo product codes. These codes involve block codes arranged as rows and columns in a rectangular array of bits. The decoder is similar to that for PCCCs and SCCCs, except that the constituent decoders are typically suboptimal soft-in/soft-out list decoders. The reader is advised to consult the leading papers in the field for additional information on the codes considered in this chapter: [4–19]. Our focus is on the binary-input AWGN channel. Nonbinary turbo codes for the noncoherent reception of orthogonal signals are considered in [20].

Many channels, such as wireless, magnetic recording, and jammed channels, tend to suffer from time intervals during which their reliability deteriorates significantly, to a degree that compromises data integrity. In some scenarios, receivers are able to detect the presence of these time intervals and may choose, accordingly, to “erase” some (or all of the) symbols received during such intervals. This technique causes symbol losses at known locations. This chapter is devoted to LDPC codes for correcting (or recovering) transmitted symbols that have been erased, called erasures. The simplest channel model with erasures is the binary erasure channel over which a transmitted bit is either correctly received or erased. There are two basic types of binary erasure channel, random and burst. Over a random binary erasure channel (BEC), erasures occur at random locations, each with the same probability of occurrence, whereas over a binary burst erasure channel (BBEC), erasures cluster into bursts. In this chapter, we first show that the LDPC codes constructed in Chapters 10–12, besides performing well over the AWGN channel, also perform well over the BEC. Then, we construct LDPC codes for correcting bursts of erasures. A list of references on LDPC codes for the binary erasure channels is given at the end of this chapter.

Iterative Decoding of LDPC Codes for the BEC

For transmission over the BEC, a transmitted symbol, 0 or 1, is either correctly received with probability 1 – p or erased with probability p, called the erasure probability, as shown in Figure 13.1.

This is the chapter where the reader first approaches the world of networks. The preliminary step to take consists in providing a succinct introduction to the analysis of the signals that, either in the electrical or in the optical domain, carry data information across networks.

Also, before throwing onto the floor the first Lego bricks and the instructions to let the reader build the composite view of modern computer networks, a review of the “fabric” of these bricks is needed. A light excursus is thus provided, to gain a basic acquaintance with copper wires, fiber optics and the radio channel, each transmission medium being employed in specific networking contexts.

Network classification comes next: it is a useful exercise to gain familiarity with the main ideas and the terminology peculiar to the world of networks. This is followed by the introduction of the crucial notion of delay, as well as by a miscellanea of concepts that cross different areas, spanning from sources of network traffic to service classification, from performance metrics to quality of service.

Following a pattern that will shape the exposition throughout the entire book, a direct experience is proposed and commented at the end of the chapter, to let the reader confront the real world via a first-hand adventure.

Signals: time and frequency analysis

Indeed, our aim is to talk about networks. Before doing so, however, we have to recall the fundamentals of signal analysis, to understand what type of information we are moving around.

The previous chapter examined code properties responsible for the floor region (high-SNR region) of LDPC and turbo codes. Specifically, the emphasis was on the computation of various weight enumerators for LDPC and turbo code ensembles because a poor weight spectrum leads to poor performance in a code's floor region both for iterative decoders and for maximum-likelihood decoders. That chapter also introduced ensemble enumerators for trapping sets and stopping sets, both of which can lead to poor floor performance in iterative decoders. In this chapter we examine the iterative decoding performance of LDPC and turbo code ensembles in the complementary low-SNR region, the “waterfall” region. We show that the iterative decoding of long LDPC and turbo codes displays a threshold effect in which communication is reliable beyond this threshold and unreliable below it. The threshold is a function of code ensemble properties and the tools introduced in this chapter allow the designer to predict the decoding threshold and its gap from Shannon's limit. The ensemble properties for LDPC codes are the degree distributions which are typically the design targets for the code-design techniques presented in subsequent chapters. The ensemble properties for turbo codes are the selected constituent codes. Our development borrows heavily from the references listed at the end of the chapter and our focus is on the binary-input AWGN channel. The references and the problems consider other channels.

Density Evolution for Regular LDPC Codes

We first summarize the main results of [1] with regard to iterative (message passing) decoding of long, regular LDPC codes.

There are two structurally different types of codes, block and convolutional codes. Both types of codes have been widely used for error control in communication and/or storage systems. Block codes can be divided into two categories, linear and nonlinear block codes. Nonlinear block codes are never used in practical applications and not much investigated. This chapter gives an introduction to linear block codes. The coverage of this chapter includes (1) fundamental concepts and structures of linear block codes; (2) specifications of these codes in terms of their generator and parity-check matrices; (3) their error-correction capabilities; (4) several important classes of linear block codes; and (5) encoding of two special classes of linear block codes, namely cyclic and quasi-cyclic codes. In our presentation, no proofs or derivations are provided; only descriptions and constructions of codes are given. We will begin our introduction with linear block codes with symbols from the binary field GF(2). Linear block codes over nonbinary fields will be given at the end of this chapter.

There are many excellent texts on the subject of error-control coding theory [1–15], which have extensive coverage of linear block codes. For in-depth study of linear block codes, readers are referred to these texts.

Introduction to Linear Block Codes

We assume that the output of an information source is a continuous sequence of binary symbols over GF(2), called an information sequence.

This final chapter is dedicated to a brief overview of some of the most important solutions used by network operators, on the one hand, for providing access to their customers, on the other, as wide area network (WAN) technologies are adopted in the network core. The chapter starts with an overview of the xDSL family, one of the most popular access technologies adopted today. Then a historical perspective of WAN technologies is given, going from the X.25 and ISDN solutions to the more recent frame relay service and ATM protocol. The attempt made by IETF to join the flexibility of the connectionless IP world with the advantages of the connection-oriented ATM approach is, finally, the basis for introducing the principles of MPLS, a very popular technology currently used by operators to offer enhanced IP-based connectivity services to their customers, including quality of service guarantees and tunneling capabilities. Given the importance of the last topic, the chapter closes with a section dedicated to a practical example of MPLS router configuration.

The xDSL family

The xDSL acronym refers to a set of solutions and technologies developed for supporting the transmission of high speed data in existing copper access networks. It also supports data transmissions at long distances but at lower bit rates.

The ITU-T recommendation G.995.1 [91] provides an overview of the digital subscriber line family. In the following ADSL, with the recent ADSL2 and ADSL2+, HDSL, SHDSL, VDSL and VDSL2 will be presented.

In Chapter 6, the main functions and architectures of routers have been presented and discussed. Routers are the basic active devices employed in networks and their fundamental task is to forward packets from node to node toward their final destination, taking the most adequate decisions concerning the network path to follow [65]. More specifically, routers perform three main functions: routing table creation and update, table look-up for forwarding decision and physical datagram forwarding from input ports to output ports.

The first of these functions is called routing and consists of running algorithms and implementing protocols suitable to the specific routing problem and network topology size [81].On the one hand, routing algorithms are executed to create and maintain routing tables, once sufficient information about the network topology has been gathered. On the other hand, routing protocols are employed between routers to exchange the network topology information necessary for executing the algorithms.

This chapter illustrates the basic principles of routing, describing the most important algorithms and protocols. The hierarchical approach to the routing problem adopted by the Internet is also discussed, including a brief overview of the most popular IP routing protocols, namely RIP and OSPF. A couple of practical examples of IP routing configurations conclude the chapter.

Routing algorithms

Routing algorithms are characterized by the way the routing table is created and possibly updated. Generally speaking, such an algorithm should be correct, fair, stable, optimal, fast, simple, and adaptive to network topology changes and to traffic conditions. It is evidently difficult to meet all these requirements with just a single, ideal algorithm, so any real routing algorithm usually provides a trade-off on some of them.