Data Communications Networking Devices - 4th Ed.pdf

1.12 ERROR DETECTION AND CORRECTION _________________________________________ 57When dissimilar CRC generating polynomials are employed,the two-byteblock-check character appended to the transmitted data block will never equal theblock-check character computed at the receiver. This will result in eachtransmitted data block being negatively acknowledged,eventually resulting in athreshold of negative acknowledgements being reached. When this threshold isreached the protocol aborts the transmission session,causing the terminal operatorto reinitiate the communications procedure required to access the computer systemthey wish to connect to. Although the solution to this problem requires either theterminal or a port on the computer system to be changed to use the appropriategenerating polynomial,the lack of publication of the fact that there are differentgenerating polynomials has caused many organizations to expend a considerableamount of needless effort. One bank which the author is familiar with monitoredtransmission attempts for almost 3 weeks. During this period,they observed eachblock being negatively acknowledged and blamed the communications carrier,insisting that the quality of the circuit was the culprit. Only after a consultant wascalled and spent approximately a week examining the situation was the problemtraced to the utilization of dissimilar generating polynomials.Forward error correctingDuring the 1950s and 1960s when mainframe computers used core memorycircuits,designers spent a considerable amount of effort developing codes thatcarried information which enabled errors to be detected and corrected. Such codesare collectively called forward error correction FEC) and have been employed inTrellis Coded Modulation modems under the ITU-T V.32,V.32 bis,V.33,andV.34 recommendation,and will be described later in this book.One popular example of a forward error correcting code is the Hamming code.This code can be used to detect one or more bits in error at a receiver as well as todetermine which bits are in error. Since a bit can have only one of two values,knowledge that a bit is in error allows the receiver to reverse or reset the bit,correcting its erroneous condition.The Hamming code uses m parity bits with a message length of n bits,wheren ˆ 2 m 1. This permits k information bits where k ˆ n m. The parity bits arethen inserted into the message at bit positions 2 j 1 where j ˆ 1; 2; ...; m. Table1.17 illustrates the use of a Hamming code error correction for m ˆ 3, k ˆ 4,andn ˆ 7.In the Hamming code encoding process the data and parity bits are exclusive-ORed with all possible data values to determine the value of each parity bit. This isillustrated in Figure 1.30 which results in P 1 ,P 2 ,and P 3 having values of 0,1,and1,respectively.Table 1.17Hamming code error correction exampleMessage length ˆ 7 bitsInformation bits ˆ 4 bits ˆ 1100Parity ˆ 3 bits ˆ P 1 ; P 2 ; P 3