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the `Physical layer service` may deliver `more` bits to the receiver than the bits sent by the sender
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:math:`10^{12}`
To understand some of the principles behind the physical transmission of information, let us consider the simple case of an electrical wire that is used to transmit bits. Assume that the two communicating hosts want to transmit one thousand bits per second. To transmit these bits, the two hosts can agree on the following rules :
On the sender side :
set the voltage on the electrical wire at ``+5V`` during one millisecond to transmit a bit set to `1`
set the voltage on the electrical wire at ``-5V`` during one millisecond to transmit a bit set to `0`
On the receiver side :
every millisecond, record the voltage applied on the electrical wire. If the voltage is set to ``+5V``, record the reception of bit `1`. Otherwise, record the reception of bit `0`
This transmission scheme has been used in some early networks. We use it as a basis to understand how hosts communicate. From a Computer Science viewpoint, dealing with voltages is unusual. Computer scientists frequently rely on models that enable them to reason about the issues that they face without having to consider all implementation details. The physical transmission scheme described above can be represented by using a `time-sequence diagram`.
With the above transmission scheme, a bit is transmitted by setting the voltage on the electrical cable to a specific value during some period of time. We have seen that due to electromagnetic interference, the voltage measured by the receiver can differ from the voltage set by the transmitter. This is the main cause of transmission errors. However, this is not the only type of problem that can occur. Besides defining the voltages for bits `0` and `1`, the above transmission scheme also specifies the duration of each bit. If one million bits are sent every second, then each bit lasts 1 microsecond. On each host, the transmission (resp. the reception) of each bit is triggered by a local clock having a 1 MHz frequency. These clocks are the second source of problems when transmitting bits over a wire. Although the two clocks have the same specification, they run on different hosts, possibly at a different temperature and with a different source of energy. In practice, it is possible that the two clocks do not operate at exactly the same frequency. Assume that the clock of the transmitting host operates at exactly 1000000 Hz while the receiving clock operates at 999999 Hz. This is a very small difference between the two clocks. However, when using the clock to transmit bits, this difference is important. With its 1000000 Hz clock, the transmitting host will generate one million bits during a period of one second. During the same period, the receiving host will sense the wire 999999 times and thus will receive one bit less than the bits originally transmitted. This small difference in clock frequencies implies that bits can "disappear" during their transmission on an electrical cable. This is illustrated in the figure below.
A similar reasoning applies when the clock of the sending host is slower than the clock of the receiving host. In this case, the receiver will sense more bits than the bits that have been transmitted by the sender. This is illustrated in the figure below where the second bit received on the right was not transmitted by the left host.
the `Physical layer service` may change, e.g. due to electromagnetic interference, the value of a bit being transmitted
the `Physical layer service` may deliver `more` bits to the receiver than the bits sent by the sender
the `Physical layer service` may deliver `fewer` bits to the receiver than the bits sent by the sender
Many other types of encodings have been defined to transmit information over an electrical cable. All physical layers are able to send and receive physical symbols that represent values `0` and `1`. However, for various reasons that are outside the scope of this chapter, several physical layers exchange other physical symbols as well. For example, the Manchester encoding used in several physical layers can send four different symbols. The Manchester encoding is a differential encoding scheme in which time is divided into fixed-length periods. Each period is divided in two halves and two different voltage levels can be applied. To send a symbol, the sender must set one of these two voltage levels during each half period. To send a `1` (resp. `0`), the sender must set a high (resp. low) voltage during the first half of the period and a low (resp. high) voltage during the second half. This encoding ensures that there will be a transition at the middle of each period and allows the receiver to synchronize its clock to the sender's clock. Apart from the encodings for `0` and `1`, the Manchester encoding also supports two additional symbols : `InvH` and `InvB` where the same voltage level is used for the two half periods. By definition, these two symbols cannot appear inside a frame which is only composed of `0` and `1`. Some technologies use these special symbols as markers for the beginning or end of frames.
Manchester encoding
All the functions related to the physical transmission or information through a wire (or a wireless link) are usually known as the `physical layer`. The physical layer allows thus two or more entities that are directly attached to the same transmission medium to exchange bits. Being able to exchange bits is important as virtually any information can be encoded as a sequence of bits. Electrical engineers are used to processing streams of bits, but computer scientists usually prefer to deal with higher level concepts. A similar issue arises with file storage. Storage devices such as hard-disks also store streams of bits. There are hardware devices that process the bit stream produced by a hard-disk, but computer scientists have designed filesystems to allow applications to easily access such storage devices. These filesystems are typically divided into several layers as well. Hard-disks store sectors of 512 bytes or more. Unix filesystems group sectors in larger blocks that can contain data or `inodes` representing the structure of the filesystem. Finally, applications manipulate files and directories that are translated in blocks, sectors and eventually bits by the operating system.
Computer networks use a similar approach. Each layer provides a service that is built above the underlying layer and is closer to the needs of the applications. The datalink layer builds upon the service provided by the physical layer. We will see that it also contains several functions.
The datalink layer
To enable the transmission/reception of frames, the first problem to be solved is how to encode a frame as a sequence of bits, so that the receiver can easily recover the received frame despite the limitations of the physical layer.
If the physical layer were perfect, the problem would be very simple. We would simply need to define how to encode each frame as a sequence of consecutive bits. The receiver would then easily be able to extract the frames from the received bits. Unfortunately, the imperfections of the physical layer make this framing problem slightly more complex. Several solutions have been proposed and are used in practice in different network technologies.
Framing
The `framing` problem can be defined as : "`How does a sender encode frames so that the receiver can efficiently extract them from the stream of bits that it receives from the physical layer`".
A first solution to this problem is to require the physical layer to remain idle for some time after the transmission of each frame. These idle periods can be detected by the receiver and serve as a marker to delineate frame boundaries. Unfortunately, this solution is not acceptable for two reasons. First, some physical layers cannot remain idle and always need to transmit bits. Second, inserting an idle period between frames decreases the maximum bit rate that can be achieved.
Bit rate and bandwidth
Bit rate and bandwidth are often used to characterize the transmission capacity of the physical service. The original definition of `bandwidth <https://www.merriam-webster.com/dictionary/bandwidth>`_, as listed in the `Webster dictionary <https://www.merriam-webster.com/dictionary>`_ is `a range of radio frequencies which is occupied by a modulated carrier wave, which is assigned to a service, or over which a device can operate`. This definition corresponds to the characteristics of a given transmission medium or receiver. For example, the human ear is able to decode sounds in roughly the 0-20 KHz frequency range. By extension, bandwidth is also used to represent the capacity of a communication system in bits per second. For example, a Gigabit Ethernet link is theoretically capable of transporting one billion bits per second.

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