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Received bits
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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.
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 :
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
a `payload` that contains the user data
Some headers also include a `length` field, which indicates the total length of the frame or the length of the payload.
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.
Checksums, CRCs,...
Most of the protocols in the TCP/IP protocol suite rely on the simple Internet checksum in order to verify that a received packet has not been affected by transmission errors. Despite its popularity and ease of implementation, the Internet checksum is not the only available checksum mechanism. Cyclical Redundancy Checks (CRC_) are very powerful error detection schemes that are used notably on disks, by many datalink layer protocols and file formats such as ``zip`` or ``png``. They can easily be implemented efficiently in hardware and have better error-detection capabilities than the Internet checksum [SGP98]_ . However, CRCs are sometimes considered to be too CPU-intensive for software implementations and other checksum mechanisms are preferred. The TCP/IP community chose the Internet checksum, the OSI community chose the Fletcher checksum [Sklower89]_. Nowadays there are efficient techniques to quickly compute CRCs in software [Feldmeier95]_.
Since the receiver sends an acknowledgment after having received each data frame, the simplest solution to deal with losses is to use a retransmission timer. When the sender sends a frame, it starts a retransmission timer. The value of this retransmission timer should be larger than the `round-trip-time`, i.e. the delay between the transmission of a data frame and the reception of the corresponding acknowledgment. When the retransmission timer expires, the sender assumes that the data frame has been lost and retransmits it. This is illustrated in the figure below.
Unfortunately, retransmission timers alone are not sufficient to recover from losses. Let us consider, as an example, the situation depicted below where an acknowledgment is lost. In this case, the sender retransmits the data frame that has not been acknowledged. However, as illustrated in the figure below, the receiver considers the retransmission as a new frame whose payload must be delivered to its user.
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).
The Alternating Bit Protocol uses a single bit to encode the sequence number. It can be implemented easily. The sender (resp. the receiver) only require a four-state (resp. three-state) Finite State Machine.
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.
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.
Dealing with corrupted frames
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.
The figure below illustrates the operation of the alternating bit protocol.
The Alternating Bit Protocol can recover from the losses of data or control frames. This is illustrated in the two figures below. The first figure shows the loss of one data frame.
The second figure illustrates how the hosts handle the loss of one control frame.
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 !
Go-back-n and selective repeat
To overcome the performance limitations of the alternating bit protocol, reliable protocols rely on `pipelining`. This technique allows a sender to transmit several consecutive frames without being forced to wait for an acknowledgment after each frame. Each data frame contains a sequence number encoded as an `n` bits field.
Pipelining improves the performance of reliable protocols
`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.
This is implemented by using a `sliding window`. The sliding window is the set of consecutive sequence numbers that the sender can use when transmitting frames without being forced to wait for an acknowledgment. The figure below shows a sliding window containing five frames (`6,7,8,9` and `10`). Two of these sequence numbers (`6` and `7`) have been used to send frames and only three sequence numbers (`8`, `9` and `10`) remain in the sliding window. The sliding window is said to be closed once all sequence numbers contained in the sliding window have been used.
The sliding window
The figure below illustrates the operation of the sliding window. It uses a sliding window of three frames. The sender can thus transmit three frames before being forced to wait for an acknowledgment. The sliding window moves to the higher sequence numbers upon the reception of each acknowledgment. When the first acknowledgment (`OK0`) is received, it enables the sender to move its sliding window to the right and sequence number `3` becomes available. This sequence number is used later to transmit the frame containing `d`.
Sliding window example
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.

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34663 String information

Component
cnp3-ebook/principles/reliability
Flags
read-only
Source string location
../../principles/reliability.rst:645
String age
6 years ago
Last updated
4 months ago
Source string age
6 years ago
Translation file
locale/pot/principles/reliability.pot, string 156