en	Connecting two hosts

en	This is an unpolished draft of the third edition of this e-book. If you find any error or have suggestions to improve the text, please create an issue via https://github.com/CNP3/ebook/issues?milestone=1 or help us by providing pull requests to close the existing issues.

en	The first step when building a network, even a worldwide network such as the Internet, is to connect two hosts together. This is illustrated in the figure below.

en	To enable the two hosts to exchange information, they need to be linked together by some kind of physical media. Computer networks have used various types of physical media to exchange information, notably :

en	`electrical cable`. Information can be transmitted over different types of electrical cables. The most common ones are the twisted pairs (that are used in the telephone network, but also in enterprise networks) and the coaxial cables (that are still used in cable TV networks, but are no longer used in enterprise networks). Some networking technologies operate over the classical electrical cable.

en	`wireless`. In this case, a radio signal is used to encode the information exchanged between the communicating devices. Many types of modulation techniques are used to send information over a wireless channel and there is lot of innovation in this field with new techniques appearing every year. While most wireless networks rely on radio signals, some use a laser that sends light pulses to a remote detector. These optical techniques allow to create point-to-point links while radio-based techniques can be used to build networks containing devices spread over a small geographical area.

en	The physical layer

en	Bit rate

en	Bits per second

en	1 Kbps

en	:math:`10^3`

en	1 Mbps

en	:math:`10^6`

en	1 Gbps

en	:math:`10^9`

en	1 Tbps

en	:math:`10^{12}`

en	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 :

en	On the sender side :

en	set the voltage on the electrical wire at ``+5V`` during one millisecond to transmit a bit set to `1`

en	set the voltage on the electrical wire at ``-5V`` during one millisecond to transmit a bit set to `0`

en	On the receiver side :

en	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`

en	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`.

en	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.

en	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.

en	the `Physical layer service` may change, e.g. due to electromagnetic interference, the value of a bit being transmitted

en	the `Physical layer service` may deliver `more` bits to the receiver than the bits sent by the sender

en	the `Physical layer service` may deliver `fewer` bits to the receiver than the bits sent by the sender

en	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.

en	Manchester encoding

en	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.

en	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.

en	The datalink layer

en	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.

en	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.

en	Framing

en	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`".

en	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.

en	Bit rate and bandwidth

en	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.

en	Given that multi-symbol encodings cannot be used by all physical layers, a generic solution which can be used with any physical layer that is able to transmit and receive only bits `0` and `1` is required. This generic solution is called `stuffing` and two variants exist : `bit stuffing` and `character stuffing`. To enable a receiver to easily delineate the frame boundaries, these two techniques reserve special bit strings as frame boundary markers and encode the frames so that these special bit strings do not appear inside the frames.

en	`Bit stuffing` reserves the `01111110` bit string as the frame boundary marker and ensures that there will never be six consecutive `1` symbols transmitted by the physical layer inside a frame. With bit stuffing, a frame is sent as follows. First, the sender transmits the marker, i.e. `01111110`. Then, it sends all the bits of the frame and inserts an additional bit set to `0` after each sequence of five consecutive `1` bits. This ensures that the sent frame never contains a sequence of six consecutive bits set to `1`. As a consequence, the marker pattern cannot appear inside the frame sent. The marker is also sent to mark the end of the frame. The receiver performs the opposite to decode a received frame. It first detects the beginning of the frame thanks to the `01111110` marker. Then, it processes the received bits and counts the number of consecutive bits set to `1`. If a `0` follows five consecutive bits set to `1`, this bit is removed since it was inserted by the sender. If a `1` follows five consecutive bits sets to `1`, it indicates a marker if it is followed by a bit set to `0`. The table below illustrates the application of bit stuffing to some frames.

en	Original frame

en	Transmitted frame

en	0001001001001001001000011

en	01111110000100100100100100100001101111110

en	0110111111111111111110010

en	01111110011011111011111011111011001001111110

en	01111110

en	0111111001111101001111110

en	For example, consider the transmission of `0110111111111111111110010`. The sender will first send the `01111110` marker followed by `011011111`. After these five consecutive bits set to `1`, it inserts a bit set to `0` followed by `11111`. A new `0` is inserted, followed by `11111`. A new `0` is inserted followed by the end of the frame `110010` and the `01111110` marker.

en	`Bit stuffing` increases the number of bits required to transmit each frame. The worst case for bit stuffing is of course a long sequence of bits set to `1` inside the frame. If transmission errors occur, stuffed bits or markers can be in error. In these cases, the frame affected by the error and possibly the next frame will not be correctly decoded by the receiver, but it will be able to resynchronize itself at the next valid marker.

en	`Bit stuffing` can be easily implemented in hardware. However, implementing it in software is difficult given the complexity of performing bit manipulations in software. Software implementations prefer to process characters than bits, software-based datalink layers usually use `character stuffing`. This technique operates on frames that contain an integer number of characters. In computer networks, characters are usually encoded by relying on the :term:`ASCII` table. This table defines the encoding of various alphanumeric characters as a sequence of bits. :rfc:`20` provides the ASCII table that is used by many protocols on the Internet. For example, the table defines the following binary representations :

en	`A` : `1000011` b

en	`0` : `0110000` b

en	`z` : `1111010` b

en	`@` : `1000000` b

en	`space` : `0100000` b

en	In addition, the :term:`ASCII` table also defines several non-printable or control characters. These characters were designed to allow an application to control a printer or a terminal. These control characters include `CR` and `LF`, that are used to terminate a line, and the `BEL` character which causes the terminal to emit a sound.

en	`NUL`: `0000000` b

en	`BEL`: `0000111` b

en	`CR` : `0001101` b

en	`LF` : `0001010` b

en	`DLE`: `0010000` b

en	`STX`: `0000010` b

en	`ETX`: `0000011` b

en	Some characters are used as markers to delineate the frame boundaries. Many `character stuffing` techniques use the `DLE`, `STX` and `ETX` characters of the ASCII character set. `DLE STX` (resp. `DLE ETX`) is used to mark the beginning (end) of a frame. When transmitting a frame, the sender adds a `DLE` character after each transmitted `DLE` character. This ensures that none of the markers can appear inside the transmitted frame. The receiver detects the frame boundaries and removes the second `DLE` when it receives two consecutive `DLE` characters. For example, to transmit frame `1 2 3 DLE STX 4`, a sender will first send `DLE STX` as a marker, followed by `1 2 3 DLE`. Then, the sender transmits an additional `DLE` character followed by `STX 4` and the `DLE ETX` marker.

en	**1** **2** **3** **4**

en	`DLE STX` **1** **2** **3** **4** `DLE ETX`

en	**1** **2** **3** **DLE** **STX** **4**

en	`DLE STX` **1** **2** **3** **DLE** `DLE` **STX** `4` `DLE ETX`

en	**DLE STX DLE ETX**

en	`DLE STX` **DLE** `DLE` **STX** **DLE** `DLE` ETX** `DLE ETX`

en	Recovering from transmission errors

en	In this section, we develop a reliable datalink protocol running above the physical layer service. To design this protocol, we first assume that the physical layer provides a perfect service. We will then develop solutions to recover from the transmission errors.

en	The datalink layer is designed to send and receive frames on behalf of a user. We model these interactions by using the `DATA.req` and `DATA.ind` primitives. However, to simplify the presentation and to avoid confusion between a `DATA.req` primitive issued by the user of the datalink layer entity, and a `DATA.req` issued by the datalink layer entity itself, we will use the following terminology :

en	the interactions between the user and the datalink layer entity are represented by using the classical `DATA.req` and the `DATA.ind` primitives

en	the interactions between the datalink layer entity and the framing sub-layer are represented by using `send` instead of `DATA.req` and `recvd` instead of `DATA.ind`

en	To solve this problem, a reliable protocol must include a feedback mechanism that allows the receiver to inform the sender that it has processed a frame and that another one can be sent. This feedback is required even though there are no transmission errors. To include such a feedback, our reliable protocol must process two types of frames :

en	data frames carrying a SDU

en	These two types of frames can be distinguished by dividing the frame in two parts :

en	the `header` that contains one bit set to `0` in data frames and set to `1` in control frames

en	the payload that contains the SDU supplied by the application

en	The datalink entity can then be modeled as a finite state machine, containing two states for the receiver and two states for the sender. The figure below provides a graphical representation of this state machine with the sender above and the receiver below.

en	The above FSM shows that the sender has to wait for an acknowledgment from the receiver before being able to transmit the next SDU. The figure below illustrates the exchange of a few frames between two hosts.

en	Services and protocols

en	Reliable data transfer on top of an imperfect link

en	The datalink layer must deal with the transmission errors. In practice, we mainly have to deal with two types of errors in the datalink layer :

en	Frames can be corrupted by transmission errors

en	Frames can be lost or unexpected frames can appear

en	To deal with these types of imperfections, reliable protocols rely on different types of mechanisms. The first problem is transmission errors. Data transmission on a physical link can be affected by the following errors :

en	random isolated errors where the value of a single bit has been modified due to a transmission error

en	random burst errors where the values of `n` consecutive bits have been changed due to transmission errors

en	random bit creations and random bit removals where bits have been added or removed due to transmission errors

en	The only solution to protect against transmission errors is to add redundancy to the frames that are sent. `Information Theory` defines two mechanisms that can be used to transmit information over a transmission channel affected by random errors. These two mechanisms add redundancy to the transmitted information, to allow the receiver to detect or sometimes even correct transmission errors. A detailed discussion of these mechanisms is outside the scope of this chapter, but it is useful to consider a simple mechanism to understand its operation and its limitations.

en	`Information theory` defines `coding schemes`. There are different types of coding schemes, but let us focus on coding schemes that operate on binary strings. A coding scheme is a function that maps information encoded as a string of `m` bits into a string of `n` bits. The simplest coding scheme is the (even) parity coding. This coding scheme takes an `m` bits source string and produces an `m+1` bits coded string where the first `m` bits of the coded string are the bits of the source string and the last bit of the coded string is chosen such that the coded string will always contain an even number of bits set to `1`. For example :

en	`1001` is encoded as `10010`

en	`1101` is encoded as `11011`

en	This parity scheme has been used in some RAMs as well as to encode characters sent over a serial line. It is easy to show that this coding scheme allows the receiver to detect a single transmission error, but it cannot correct it. However, if two or more bits are in error, the receiver may not always be able to detect the error.

en	Some coding schemes allow the receiver to correct some transmission errors. For example, consider the coding scheme that encodes each source bit as follows :

en	`1` is encoded as `111`

en	`0` is encoded as `000`

en	For example, consider a sender that sends `111`. If there is one bit in error, the receiver could receive `011` or `101` or `110`. In these three cases, the receiver will decode the received bit pattern as a `1` since it contains a majority of bits set to `1`. If there are two bits in error, the receiver will not be able anymore to recover from the transmission error.

en	To understand `error detection codes`, let us consider two devices that exchange bit strings containing `N` bits. To allow the receiver to detect a transmission error, the sender converts each string of `N` bits into a string of `N+r` bits. Usually, the `r` redundant bits are added at the beginning or the end of the transmitted bit string, but some techniques interleave redundant bits with the original bits. An `error detection code` can be defined as a function that computes the `r` redundant bits corresponding to each string of `N` bits. The simplest error detection code is the parity bit. There are two types of parity schemes : even and odd parity. With the `even` (resp. `odd`) parity scheme, the redundant bit is chosen so that an even (resp. odd) number of bits are set to `1` in the transmitted bit string of `N+r` bits. The receiver can easily recompute the parity of each received bit string and discard the strings with an invalid parity. The parity scheme is often used when 7-bit characters are exchanged. In this case, the eighth bit is often a parity bit. The table below shows the parity bits that are computed for bit strings containing three bits.

en	3 bits string

en	Odd parity

en	Even parity

en	000

en	1

en	0

en	001

en	010

en	100

en	111

en	110

en	101

en	011

en	The parity bit allows a receiver to detect transmission errors that have affected a single bit among the transmitted `N+r` bits. If there are two or more bits in error, the receiver may not necessarily be able to detect the transmission error. More powerful error detection schemes have been defined. The Cyclical Redundancy Checks (CRC) are widely used in datalink layer protocols. An N-bits CRC can detect all transmission errors affecting a burst of less than N bits in the transmitted frame and all transmission errors that affect an odd number of bits. Additional details about CRCs may be found in [Williams1993]_.

en	It is also possible to design a code that allows the receiver to correct transmission errors. The simplest `error correction code` is the triple modular redundancy (TMR). To transmit a bit set to `1` (resp. `0`), the sender transmits `111` (resp. `000`). When there are no transmission errors, the receiver can decode `111` as `1`. If transmission errors have affected a single bit, the receiver performs majority voting as shown in the table below. This scheme allows the receiver to correct all transmission errors that affect a single bit.

en	Received bits

en	Decoded bit

en	Other more powerful error correction codes have been proposed and are used in some applications. The `Hamming Code <https://en.wikipedia.org/wiki/Hamming_code>`_ is a clever combination of parity bits that provides error detection and correction capabilities.

en	Reliable protocols use error detection schemes, but none of the widely used reliable protocols rely on error correction schemes. To detect errors, a frame is usually divided into two parts :

en	a `header` that contains the fields used by the reliable protocol to ensure reliable delivery. The header contains a checksum or Cyclical Redundancy Check (CRC) [Williams1993]_ that is used to detect transmission errors

en	a `payload` that contains the user data

en	Some headers also include a `length` field, which indicates the total length of the frame or the length of the payload.

en	The simplest error detection scheme is the checksum. A checksum is basically an arithmetic sum of all the bytes that a frame is composed of. There are different types of checksums. For example, an eight bit checksum can be computed as the arithmetic sum of all the bytes of (both the header and trailer of) the frame. The checksum is computed by the sender before sending the frame and the receiver verifies the checksum upon frame reception. The receiver discards frames received with an invalid checksum. Checksums can be easily implemented in software, but their error detection capabilities are limited. Cyclical Redundancy Checks (CRC) have better error detection capabilities [SGP98]_, but require more CPU when implemented in software.

en	To solve this problem, datalink protocols associate a `sequence number` to each data frame. This `sequence number` is one of the fields found in the header of data frames. We use the notation `D(x,...)` to indicate a data frame whose sequence number field is set to value `x`. The acknowledgments also contain a sequence number indicating the data frames that it is acknowledging. We use `OKx` to indicate an acknowledgment frame that confirms the reception of `D(x,...)`. The sequence number is encoded as a bit string of fixed length. The simplest reliable protocol is the Alternating Bit Protocol (ABP).

en	The initial state of the sender is `Wait for D(0,...)`. In this state, the sender waits for a `Data.request`. The first data frame that it sends uses sequence number `0`. After having sent this frame, the sender waits for an `OK0` acknowledgment. A frame is retransmitted upon expiration of the retransmission timer or if an acknowledgment with an incorrect sequence number has been received.

en	The receiver first waits for `D(0,...)`. If the frame contains a correct `CRC`, it passes the SDU to its user and sends `OK0`. If the frame contains an invalid CRC, it is immediately discarded. Then, the receiver waits for `D(1,...)`. In this state, it may receive a duplicate `D(0,...)` or a data frame with an invalid CRC. In both cases, it returns an `OK0` frame to allow the sender to recover from the possible loss of the previous `OK0` frame.

en	Dealing with corrupted frames

en	The receiver FSM of the Alternating bit protocol discards all frames that contain an invalid CRC. This is the safest approach since the received frame can be completely different from the frame sent by the remote host. A receiver should not attempt at extracting information from a corrupted frame because it cannot know which portion of the frame has been affected by the error.

en	The figure below illustrates the operation of the alternating bit protocol.

en	The Alternating Bit Protocol can recover from transmission errors and frame losses. However, it has one important drawback. Consider two hosts that are directly connected by a 50 Kbits/sec satellite link that has a 250 milliseconds propagation delay. If these hosts send 1000 bits frames, then the maximum throughput that can be achieved by the alternating bit protocol is one frame every :math:`20+250+250=520` milliseconds if we ignore the transmission time of the acknowledgment. This is less than 2 Kbits/sec !

en	Go-back-n and selective repeat

en	Pipelining improves the performance of reliable protocols

en	`Pipelining` allows the sender to transmit frames at a higher rate. However this higher transmission rate may overload the receiver. In this case, the frames sent by the sender will not be correctly received by their final destination. The reliable protocols that rely on pipelining allow the sender to transmit `W` unacknowledged frames before being forced to wait for an acknowledgment from the receiving entity.

en	The sliding window

en	Sliding window example

en	In practice, as the frame header includes an `n` bits field to encode the sequence number, only the sequence numbers between :math:`0` and :math:`2^{n}-1` can be used. This implies that, during a long transfer, the same sequence number will be used for different frames and the sliding window will wrap. This is illustrated in the figure below assuming that `2` bits are used to encode the sequence number in the frame header. Note that upon reception of `OK1`, the sender slides its window and can use sequence number `0` again.

en	Utilisation of the sliding window with modulo arithmetic

en	Unfortunately, frame losses do not disappear because a reliable protocol uses a sliding window. To recover from losses, a sliding window protocol must define :

en	a heuristic to detect frame losses

en	a `retransmission strategy` to retransmit the lost frames

en	The figure below shows the FSM of a simple `go-back-n` receiver. This receiver uses two variables : `lastack` and `next`. `next` is the next expected sequence number and `lastack` the sequence number of the last data frame that has been acknowledged. The receiver only accepts the frame that are received in sequence. `maxseq` is the number of different sequence numbers (:math:`2^n`).

en	The operation of `go-back-n` is illustrated in the figure below. In this figure, note that upon reception of the out-of-sequence frame `D(2,c)`, the receiver returns a cumulative acknowledgment `C(OK,0)` that acknowledges all the frames that have been received in sequence. The lost frame is retransmitted upon the expiration of the retransmission timer.

en	Go-back-n : example

en	The main advantage of `go-back-n` is that it can be easily implemented, and it can also provide good performance when only a few frames are lost. However, when there are many losses, the performance of `go-back-n` quickly drops for two reasons :

en	the `go-back-n` receiver does not accept out-of-sequence frames

en	the `go-back-n` sender retransmits all unacknowledged frames once it has detected a loss

en	`Selective repeat` is a better strategy to recover from losses. Intuitively, `selective repeat` allows the receiver to accept out-of-sequence frames. Furthermore, when a `selective repeat` sender detects losses, it only retransmits the frames that have been lost and not the frames that have already been correctly received.

en	A `selective repeat` receiver maintains a sliding window of `W` frames and stores in a buffer the out-of-sequence frames that it receives. The figure below shows a five-frame receive window on a receiver that has already received frames `7` and `9`.

en	The receiving window with selective repeat

en	A `selective repeat` receiver discards all frames having an invalid CRC, and maintains the variable `lastack` as the sequence number of the last in-sequence frame that it has received. The receiver always includes the value of `lastack` in the acknowledgments that it sends. Some protocols also allow the `selective repeat` receiver to acknowledge the out-of-sequence frames that it has received. This can be done for example by placing the list of the correctly received, but out-of-sequence frames in the acknowledgments together with the `lastack` value.

en	When a `selective repeat` receiver receives a data frame, it first verifies whether the frame is inside its receiving window. If yes, the frame is placed in the receive buffer. If not, the received frame is discarded and an acknowledgment containing `lastack` is sent to the sender. The receiver then removes all consecutive frames starting at `lastack` (if any) from the receive buffer. The payloads of these frames are delivered to the user, `lastack` and the receiving window are updated, and an acknowledgment acknowledging the last frame received in sequence is sent.

en	The `selective repeat` sender maintains a sending buffer that can store up to `W` unacknowledged frames. These frames are sent as long as the sending buffer is not full. Several implementations of a `selective repeat` sender are possible. A simple implementation associates one retransmission timer to each frame. The timer is started when the frame is sent and canceled upon reception of an acknowledgment that covers this frame. When a retransmission timer expires, the corresponding frame is retransmitted and this retransmission timer is restarted. When an acknowledgment is received, all the frames that are covered by this acknowledgment are removed from the sending buffer and the sliding window is updated.

en	The figure below illustrates the operation of `selective repeat` when frames are lost. In this figure, `C(OK,x)` is used to indicate that all frames, up to and including sequence number `x` have been received correctly.

en	Selective repeat : example

en	Pure cumulative acknowledgments work well with the `go-back-n` strategy. However, with only cumulative acknowledgments a `selective repeat` sender cannot easily determine which frames have been correctly received after a data frame has been lost. For example, in the figure above, the second `C(OK,0)` does not inform explicitly the sender of the reception of `D(2,c)` and the sender could retransmit this frame although it has already been received. A possible solution to improve the performance of `selective repeat` is to provide additional information about the received frames in the acknowledgments that are returned by the receiver. For example, the receiver could add in the returned acknowledgment the list of the sequence numbers of all frames that have already been received. Such acknowledgments are sometimes called `selective acknowledgments`. This is illustrated in the figure above.

en	In the figure above, when the sender receives `C(OK,0,[2])`, it knows that all frames up to and including `D(0,...)` have been correctly received. It also knows that frame `D(2,...)` has been received and can cancel the retransmission timer associated to this frame. However, this frame should not be removed from the sending buffer before the reception of a cumulative acknowledgment (`C(OK,2)` in the figure above) that covers this frame.

en	Maximum window size with `go-back-n` and `selective repeat`

en	A reliable protocol that uses `n` bits to encode its sequence number can send up to :math:`2^n` successive frames. However, to ensure a reliable delivery of the frames, `go-back-n` and `selective repeat` cannot use a sending window of :math:`2^n` frames. Consider first `go-back-n` and assume that a sender sends :math:`2^n` frames. These frames are received in-sequence by the destination, but all the returned acknowledgments are lost. The sender will retransmit all frames. These frames will all be accepted by the receiver and delivered a second time to the user. It is easy to see that this problem can be avoided if the maximum size of the sending window is :math:`{2^n}-1` frames. A similar problem occurs with `selective repeat`. However, as the receiver accepts out-of-sequence frames, a sending window of :math:`{2^n}-1` frames is not sufficient to ensure a reliable delivery. It can be easily shown that to avoid this problem, a `selective repeat` sender cannot use a window that is larger than :math:`\frac{2^n}{2}` frames.

en	Reliable protocols often need to send data in both directions. To reduce the overhead caused by the acknowledgments, most reliable protocols use `piggybacking`. Thanks to this technique, a datalink entity can place the acknowledgments and the receive window that it advertises for the opposite direction of the data flow inside the header of the data frames that it sends. The main advantage of piggybacking is that it reduces the overhead as it is not necessary to send a complete frame to carry an acknowledgment. This is illustrated in the figure below where the acknowledgment number is underlined in the data frames. Piggybacking is only used when data flows in both directions. A receiver will generate a pure acknowledgment when it does not send data in the opposite direction as shown in the bottom of the figure.

en	Piggybacking example

en	SDU is the acronym of Service Data Unit. We use it as a generic term to represent the data that is transported by a protocol.

en	The size of the sliding window can be either fixed for a given protocol or negotiated during the connection establishment phase. Some protocols allow to change the maximum window size during the data transfer. We will explain these techniques with real protocols later.