Introduction of Network Coding Theory

Consider a network consisting of point-to-point communication channels. Each channel transmits information noiselessly subject to the channel capacity. Data is to be transmitted from the source node to a prescribed set of destination nodes. Given the transmission requirements, a natural question is whether the network can fulfill these requirements and how it can be done efficiently. In existing computer networks, information is transmitted from the source node to each destination node through a chain of intermediate nodes by a method known as store-and-forward. In this method, data packets received from an input link of an intermediate node are stored and a copy is forwarded to the next node via an output link. In the case when an intermediate node is on the transmission paths toward multiple destinations, it sends one copy of the data packets onto each output link that leads to at least one of the destinations. It has been a folklore in data networking that there is no need for data processing at the intermediate nodes except for data replication.

Recently, the fundamental concept of network coding was first introduced for satellite communication networks in [211] and then fully

2 Introduction
developed in [158], where in the latter the term “network coding” was coined and the advantage of network coding over store-and-forward was first demonstrated, thus refuting the aforementioned folklore. Due to
its generality and its vast application potential, network coding has generated much interest in information and coding theory, networking, switching, wireless communications, complexity theory, cryptography, operations research, and matrix theory. Prior to [211] and [158], network coding problems for special networks had been studied in the context of distributed source coding [207][177][200][212][211]. The works in [158] and [211], respectively, have inspired subsequent investigations of network coding with a single information source and with multiple information sources. The theory of network coding has been developed in various directions, and new applications of network coding continue to emerge. For example, network coding technology is applied in a prototype file-sharing application [176]1. For a short introduction of the subject, we refer the reader to [173]. For an update of the literature, we refer the reader to the Network Coding Homepage [157]. The present text aims to be a tutorial on the basics of the theory of network coding. The intent is a transparent presentation without necessarily presenting all results in their full generality. Part I is devoted to network coding for the transmission from a single source node to other nodes in the network. It starts with describing examples on network coding in the next section. Part II deals with the problem under the more general circumstances when there are multiple source nodes each intending to transmit to a different set of destination nodes. Compared with the multi-source problem, the single-source network coding problem is better understood. Following [188], the best possible benefits of network coding can very much be achieved when the coding scheme is restricted to just linear transformations. Thus the tools employed in Part I are mostly algebraic. By contrast, the tools employed in Part II are mostly probabilistic. While this text is not intended to be a survey on the subject, we nevertheless provide at <http://dx.doi.org/10.1561/0100000007>

1.2 Some examples

Terminology. By a communication network we shall refer to a finite directed graph, where multiple edges from one node to another are allowed. A node without any incoming edges is called a source node. Any other node is called a non-source node. Throughout this text, in the figures, a source node is represented by a square, while a non-sourc node is represented by a circle. An edge is also called a channel and represents a noiseless communication link for the transmission of a data unit per unit time. The capacity of direct transmission from a node to a neighbor is determined by the multiplicity of the channels between them. For example, the capacity of direct transmission from the node W to the node X in Figure 1.1(a) is 2. When a channel is from a node X to a node Y , it is denoted as XY . A communication network is said to be acyclic if it contains no directed cycles. Both networks presented in Figures 1.1(a) and (b) are examples of acyclic networks. A source node generates a message, which is propagated through the network in a multi-hop fashion. We are interested in how much information and how fast it can be received by the destination nodes.

However, this depends on the nature of data processing at the nodes in relaying the information.

 Fig. 1.1 Multicasting over a communication network.

Assume that we multicast two data bits b1 and b2 from the source node S to both the nodes Y and Z in the  acyclic network depicted by Figure 1.1(a). Every channel carries either the bit b1 or the bit b2 as indicated. In this way, every intermediate node simply replicates and sends out the bit(s) received from upstream. The same network as in Figure 1.1(a) but with one less channel appears in Figures 1.1(b) and (c), which shows a way of multicasting 3 bits b1, b2 and b3 from S to the nodes Y and Z in 2 time units.This achieves a multicast rate of 1.5 bits per unit time, which is actually the maximum possible when the intermediate nodes perform just bit replication (See [209], Ch. 11, Problem 3). The network under discussion is known as the butterfly network. Example 1.1. (Network coding on the butterfly network) Figure 1.1(d) depicts a different way to multicast two bits from the source node S to Y and Z on the same network as in Figures 1.1(b) and (c). This time the node W derives from the received bits b1 and b2 the exclusive-OR bit b1  b2. The channel from W to X transmits b1  b2, which is then replicated at X for passing on to Y and Z. Then, the node Y receives b1 and b1  b2, from which the bit b2 can be decoded. Similarly, the node Z decodes the bit b1 from the received bits b2 and b1  b2. In this way, all the 9 channels in the network are used exactly once. The derivation of the exclusive-OR bit is a simple form of coding. If the same communication objective is to be achieved simply by bit replication at the intermediate nodes without coding, at least one channel in the network must be used twice so that the total number of channel usage would be at least 10. Thus, coding offers the potential advantage of minimizing both latency and energy consumption, and at the same time maximizing the bit rate.

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COAL BLASTING

Authority for regulating blasting operations at coal mines comes from the Surface Coal Mining Land Conservation and Reclamation Act (SCMLCRA), which became effective February 1, 1983. The SCMLCRA is closely patterned after the federal Surface Mining Control and Reclamation Act of 1977 (SMCRA). The SCMLCRA has established air blast, ground vibration and fly rock standards, training, examination and certification requirements for persons supervising blasting operations, requirements for pre-blast surveys and public blasting notices, requirements for the maintenance of blasting records and enforcement provisions which give the Mine Safety and Training Division the authority to suspend or revoke blasting certificates, issue notices of violation and/or cessation orders and assess civil penalties in instances of non-compliance.

In addition to blasting, the SCMLCRA contains comprehensive environmental protection requirements such as hydrologic balance protection, soil replacement and disposal of toxic materials. All aspects of the SCMLCRA,other than blasting, are administered by the Land Reclamation Division within the Office of Mines and Minerals. So why do companies employ blasting at their operations? Below you will find answers to this and other questions related to blasting at Illinois mines.

WHY DO MINING COMPANIES BLAST?

Blasting is the most cost effective way to fracture rock. Therefore, blasting reduces the costs of consumer goods such as electricity, sand, gravel, concrete, aluminum, copper and many other products manufactured from mined resources. The old statement “If it can’t be grown, it has to be mined” is still true today.

WHAT EXPLOSIVES ARE USED FOR BLASTING?

Dynamite, a nitroglycerin-based explosive, is rarely used today for blasting at surface mines in Illinois. Blasting agents account for almost 99% of the explosive materials used. ANFO, ammonium nitrate and fuel oil, is the most common explosive. ANFO, pound for pound is as powerful as dynamite and is less expensive per pound and less sensitive to initiation and therefore safer to use.

WHAT IS BLASTING?

Holes are drilled into the rock to be broken. A portion of each hole is filled with explosives. The top portion of the hole is filled with inert material called stemming. The explosive in each hole is initiated with detonators or blasting caps. The detonators are designed to create millisecond (thousandths of a second) delay periods between individual holes or charges. A blast with 25 individual holes will essentially consist of smaller individual blasts, separated by millisecond delays and the entire blast may only last ¼ - ½ of a second. When an explosive is detonated, it undergoes a very rapid decomposition which produces a large volume or expansion of gases, instantly. This expansion of gases is what causes the rock to fracture. The stemming material keeps the gases in the rock to maximize the amount of the energy utilized in the fragmentation process. The delay periods between charges ensures that each hole will only have to fragment the rock immediately in front of it, which

enhances fragmentation.

HOW FAR DOES THE FRAGMENTATION EXTEND FROM THE BLASTHOLE?

Small blastholes are usually drilled from 6 to 15 feet apart and large blastholes may range up to 30 feet apart. The fact that holes have to be drilled relatively close together is a good indicator of how far the fragmentation occurs. Even micro-fractures may only extend 40 blasthole diameters away from the blasthole. There is even less fracturing below the blasthole. This is demonstrated at surface coal mines, where only a few feet of rock separates the explosive (bottom of the blasthole) from the top of the coal seam, and protects the coal, which is a relatively weak or brittle rock, from fracturing.

WHAT IS GROUND VIBRATION?

When a blast is detonated, some of the energy travels through the ground as vibration. The ground vibration travels mainly on the surface at varying speeds depending upon the density and thickness of the geology. Although perceptible, the energy level decreases rapidly with distance. To the blaster, vibration represents wasted explosive energy. Blasting accounts for a large percentage of production costs, therefore it is to the operators advantage to maximize fragmentation by minimizing vibrations. Blasting seismographs measure ground vibrations in terms of particle velocity which is the speed at which the ground moves. Particle velocity is measured in inches per second. The peak particle velocity (PPV) which is not to be exceeded to prevent damage to homes is 1.0 inch per second. Although 1.0 inch per second sounds like a large movement of the ground, it is important to remember that this is velocity of movement and the actual displacement occurring with ground vibrations from blasting is measured in thousandths (0.001) of an inch. Ground vibrations are mainly controlled by limiting the pounds of explosives detonated per delay interval, as discussed above. For example, a 100-hole blast can be designed to have the same vibration as a 10-hole blast with the same pounds of explosives per hole and at the same distance.

WHAT IS AIRBLAST?

Airblast is a change in air pressure caused by blasting. When a blast is detonated, some of the energy is vented into the atmosphere through the fractures in the rock or through inadequate stemming material. However, the upward or outward movement of the rock from the blast is the main source of airblast. Due to the frequency content, airblast cannot be effectively heard by the human ear. Airblast travels at the speed of sound and can be influenced by wind and temperature inversions. Airblast is also measured with a blasting seismograph equipped with a special microphone. The most common units to measure airblast is decibels (dB) which is a logarithmic sound-pressure scale related to human hearing. A difference of 6 dB represents a doubling or halving of the airblast energy. Airblast is controlled by properly confining explosive charges in the borehole. This is accomplished by using adequate stemming material and by not loading explosives into weak zones in the rock. Airblast also represents wasted explosive energy. If the explosive gases escape from the blasthole, there will not be adequate energy to fragment the rock.

HOW ARE HOMES PROTECTED FROM GROUND VIBRATION AND AIRBLAST?

Many scientific studies have investigated the potential of blast vibrations to damage residential-type structures. The conclusions from these studies have been incorporated into DNR’s regulations. The blasting activities at all surface mining operations are regulated to prevent threshold or cosmetic damage (hairline cracks) to the weakest of building material. This is best accomplished with performance standards which limit peak particle velocities (ground vibration) and decibels (airblast). This is not to say that blasting limits which are designed to prevent damage will not be annoying to neighbors. Blast vibrations are perceptible to humans at much lower levels; as low as 0.02 inch per second PPV. The level of annoyance resulting from ground vibrations varies from person to person, thus making annoyance limits a poor choice for regulatory programs. Blast vibrations can be perceptible in a home at great distances from a blast. Structures respond to very low levels of ground vibration and/or airblast. It is interesting to note that the everyday environmental influences on a home, such as doors slamming, kids running in the house, running up and down stairs, pounding nails, outside temperature, wind, humidity and soil moisture changes produce strains greater than legal blasting limits. These everyday activities often go unnoticed due to the fact that they are expected whereas blast vibrations can be unexpected.

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Mine Closure

MINE CLOSURE - INTRODUCTION
 

As we progress into the twenty-first century, there is increasing awareness of the need to provide for 'sustainability' of ecological and social settings in which mines are developed, operated and closed. The 'six tenets for sustainability of mining' provide the foundation for sustainability planning at a mine site. This gives rise to the need to do more than 'Design for Closure', requiring that we also prepare 'Post Mining Sustainable Use Plans' for the mine site and affected area. This concept is described by Robertson et al., 1998 and Robertson and Shaw, 1999. It also requires that all stakeholders, including the succeeding custodian, be consulted in the preparation of mine development, operations, closure and post closure sustainable use plans.
 

An example of innovate post mining land use development is the redevelopment of an abandoned mine in Cornwall called the Eden Project. In planning for closure, there are four key objectives that must be considered:
1. protect public health and safety;
2. alleviate or eliminate environmental damage;
3. achieve a productive use of the land, or a return to its original condition or an acceptable alternative; and,
4. to the extent achievable, provide for sustainability of social and economic benefits resulting from mine development and operations.
 

Impacts that change conditions affecting these objectives are often broadly discussed as the 'impacts' or the environmental impacts of a site or a closure plan. It is convenient to consider potential impacts in four groupings:
 

1. Physical stability - buildings, structures, workings, pit slopes, underground openings etc. must be stable and not move so as to eliminate any hazard to the public health and safety or material erosion to the terrestrial or aquatic receiving environment at concentrations that are harmful. Engineered structures must not deteriorate and fail.
 

2. Geochemical stability - minerals, metals and 'other' contaminants must be stable, that is, must not leach and/or migrate into the receiving environment at concentrations that are harmful. Weathering oxidation and leaching processes must not transport contaminants, in excessive concentrations, into the environment. Surface waters and groundwater must be protected against adverse environmental impacts resulting from mining and processing activities.
 

3. Land use - the closed mine site should be rehabilitated to pre-mining conditions or conditions that are compatible with the surrounding lands or achieves an agreed alternative productive land use. Generally the former requires the land to be aesthetically similar to the surroundings and capable of supporting a self-sustaining ecosystem typical of the area.
 

4. Sustainable development - elements of mine development that contribute to (impact) the sustainability of social and economic benefit, post mining, should be maintained and transferred to succeeding custodians.
 

Clearly the assessment of these types of impacts and closure requirements must address components of the site as well as the region and must select measures and allocate resources to address the major issues of impact. In order to minimize the various impacts, risks and liabilities, it is necessary to anticipate, as early in the process as possible, potential future liabilities and risks, and to plan for their elimination or minimization. In many areas, much of the liability or risk is associated with the uncertainty of the requirements for closure and rehabilitation from the succeeding custodian (be it a government agency, community organization or corporate entity). Early identification of the succeeding custodian, and their involvement in the development of the closure plan enables the closure requirements to be established and agreed and considered in the closure plan development. This allows the mining company to determine, and provide for, the requirements of the succeeding custodians, gain their support for the closure plan and minimize the risks and liabilities that may derive from succeeding custodian rejection or objection to the closure measures at the time of mine closure.

MINE CLOSURE - STEPS IN CLOSURE PLAN DEVELOPMENT

The typical steps for closure planning are shown in Figure 1. These steps also provide a logical order in which to develop and present the various sections of a Closure Plan Report. They provide the reader with a progressive description of the material required to understand the need for, nature of, effectiveness of, and cost the Closure Plan.
 

Any closure plan must consider the long-term physical, chemical, biological and social/land-use effects on the surrounding natural systems (aquatic, groundwater, surface water etc.). Therefore there must be an understanding of the pre-mining environment (step 1) and the effects of past and future mine development (step 2) on the pre-mining environment. Operational control measures must be selected (step 3) for implementation during mining in order to minimize the impact on the surrounding ecosystems. Impact assessments (step 4) must be done prior to measures selection as well as periodically during operations in order to determine the success of the measures implemented. Alternative mine closure measures are developed (step 5) and assessed (step 6) during mine design to ensure that there are suitable closure measures available to remediate the impact of the selected mine development.
 

If suitable remediation or closure measures cannot be identified or achieved, then it may be appropriate to revise the type of mine development proposed (return to step 2). Once a technically acceptable mine development and closure plan has been developed it is necessary to prepare a monitoring and maintenance plan (step 7) that will monitor the system performance during operations and post closure and provide for the maintenance necessary to ensure the long term functionality of the system components. Throughout this process, costing and scheduling evaluations (step 8) are completed, if the costs are too onerous, or if fatal flaws in the design are identified, the process returns to the design phase (step 2) and alternative measures are evaluated
 

Once an acceptable plan is completed, an acceptable form of financial assurance is developed and provided (step 9) in order to cover the costs of plan implementation, long term operations, monitoring and maintenance of the site post closure. The final stages of the closure plan process involve the application for (step 10) and approval by (step 11) the regulatory agencies of the Closure Plan, and implementation (step 12) at the end of mine life.

Figure 1. Typical Steps in the Closure Plan Development Process.

MINE CLOSURE - CYCLIC EVALUATION OF PLANS AT VARIOUS STAGES OF A MINE'S LIFE.

Each development, operating and closure plan comprises a design with drawings; specifications that define what will be constructed, and an operating plan which describes how the constructed facilities or machines will be operated. The design is completed to satisfy a number of design criteria and the operating plan specifies a number of operating constraints. Sometimes the permit conditions specified by the regulatory authorities include certain design criteria and operating constraints.
 

During the development of the design, the design engineer is continually doing informal risk assessments (or failure mode and effects analyses - FMEAs) to check that his/her design will meet operating requirements. If the current design has unacceptable risks of not meeting the design objectives, either the design or the operating procedures are modified until adequate performance characteristics are achieved (this evaluation process is represented by the upper half of the top circle on Figure 2). It is becoming more common for large mine developments to appoint Boards of Review to provide an independent check (audit or review) of the designs and operating manuals to ensure the appropriate 'International" standards of safety and environmental impact (risk or liability) are achieved. In effect these Boards perform FMEA's within the scope of their audits or review.
 

The FMEA primarily addresses the risk of designs and operating procedures not achieving the design intent. There are a number of other assessments that are important in deciding if a particular mine development or closure option is appropriate and represents a reasonably optimized plan. These assessments include impacts on the environment, the local and distant communities, costs etc (represented by the bottom half of the top circle on Figure 2). All significant stakeholders may need to participate in all or part of these evaluations and accounts must be taken of their values and concerns. A methodology, termed the multiple accounts analysis (MAA) has been developed as one of the tools (together with EA's, EIS's or ERA's) to perform such assessments (see Robertson and Shaw, 1998; Robertson and Shaw, 1999; and Shaw et al., 2001 for more details). The end result is the selection of a preferred Closure Plan.
 

Closure plans should be re-evaluated as the mine site development progresses since the initial plans are based on projected conditions which are expected to change in response to additional ore discoveries, changing conditions of product and mining economics, advances in technology and new regulatory requirements. Once the initial plan has been developed and is accepted, periodic, iterative re-assessments and revisions should be completed to ensure that the plan remains current, relevant and optimized. This results in a cyclical development of the plan and mine design over various stages of a mine's life as illustrated in Figure 2.

Figure 2. Cyclic Development of Plans and Designs at Various Stages of a Mine's Life.

Figure 2 provides an illustration of the successive activities at various stages of a mine project's life. The mining process, and the mine closure planning process, involve stages that evolve from conceptual to feasibility to permitting to operating to closure and finally to a post closure stage. These stages are shown on the figure down the left hand side. The circle at the top of the figure illustrates the decision-making activities as discussed above that are typically involved at each stage.
 

During the period of design, operating plan development and FMEA and MAA evaluations of a Closure Plan, there will be iterative modifications to the designs and operating procedures until a revised plan is agreed. The entire process is typically repeated periodically at intervals of about 5 years to ensure that the plans always remain relevant and current.
 

The FMEA is intended to minimize risk (financial as well as environmental) associated with complex, long duration engineered systems as represented by the closure measures. The MAA provides a basis for the evaluation of impacts and tradeoffs where large, high economic value projects also have high, and potentially long term, social and environmental impacts. The MAA provides the mechanism for communication of stakeholder values, as well as the accounting system by which they can be taken into consideration in the development of control and closure plans that address concerns from all stakeholders.

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