## Error Detection

Read this material. Datalink mechanisms also help solve problems related to detecting transmission error.

##### 6.1.2 Error detection

Besides framing, datalink layers also include mechanisms to detect and sometimes even recover from transmission error. To allow a receiver to detect transmission errors, a sender must add some redundant information as an error detection code to the frame sent. This error detection code is computed by the sender on the frame that it transmits. When the receiver receives a frame with an error detection code, it recomputes it and verifies whether the received error detection code matches the computer error detection code. If they match, the frame is considered to be valid. Many error detection schemes exist and entire books have been written on the subject. A detailed discussion of these techniques is outside the scope of this book, and we will only discuss some examples to illustrate the key principles.

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.

 3 bits string Odd parity Even parity 000 001 010 100 111 110 101 011 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0

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].

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.

 Received bits Decoded bit 000 001 010 100 111 110 101 011 0 0 0 0 1 1 1 1

Other more powerful error correction codes have been proposed and are used in some applications. The Hamming Code is a clever combination of parity bits that provides error detection and correction capabilities.

In practice, datalink layer protocols combine bit stuffing or character stuffing with a length indication in the frame header and a checksum or CRC. The checksum/CRC is computed by the sender and placed in the frame before applying bit/character stuffing.