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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]_.
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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.
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Received bits
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Decoded bit
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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.
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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 :
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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
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a `payload` that contains the user data
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Some headers also include a `length` field, which indicates the total length of the frame or the length of the payload.
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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.
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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).
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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.
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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.
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Dealing with corrupted frames
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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.
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The figure below illustrates the operation of the alternating bit protocol.
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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 !
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