Data Communications Networking Devices - 4th Ed.pdf

1.12 ERROR DETECTION AND CORRECTION _________________________________________ 53Figure 1.27Multiple errors on an XMODEM data blockis computed the ASCII value of each data character is ®rst added,resulting in asum of 6272 128 49). Next,the sum is divided by 255,with the remainder usedas the checksum,which in this example is 152.Suppose two transmission impairments occur during the transmission of a datablock under the XMODEM protocol,affecting two data characters as illustrated inFigure 1.27.Here the ®rst transmission impairment converted the ASCII value of thecharacter from 49 to 48,while the second impairment converted the ASCII valueof the character from 49 to 50. Assuming no other errors occurred,the receivingdevice would add the ASCII value of each of the 128 data characters and obtain asum of 6272. When the receiver divides the sum by 255,it obtains a checksum of152,which matches the transmitted checksum and the errors remain undetected.Although the preceding illustration was contrived,it illustrates the potential forundetected errors to occur under the XMODEM protocol.To make the protocol more ef®cient with respect to undetected errors,severalderivatives of the XMODEM protocol have gained popularity and are nowcommonly available in most communications programs designed for operation onpersonal computers as well as supported by information utilities and bulletin boardsystems. These derivatives of the XMODEM protocol include XMODEM/CRCand YMODEM,each of which uses a cyclic redundancy check CRC) in place ofthe checksum for error detection. The use of CRC error detection reduces theprobability of undetected errors to less than one in a million blocks and is thepreferred method for ensuring data integrity. The concept of CRC error detectionis explained later in this section under synchronous transmission,as it was ®rstemployed with this type of transmission. The operation of the XMODEM,XMODEM/CRC and YMODEM protocols are examined in more detail in theprotocol section of this chapter.Synchronous transmissionThe majority of error-detection schemes employed in synchronous transmissioninvolve geometric codes or cyclic code. However,several modi®cations to theoriginal XMODEM protocol,such as XMODEM-CRC,use a cyclic code toprotect asynchronously transmitted data.Geometric codes attack the de®ciency of parity by extending it to twodimensions. This involves forming a parity bit on each individual character aswell as on all the characters in the block. Figure 1.28 illustrates the use of blockparity checking for a block of 10 data characters. As indicated,this block paritycharacter is also known as the `longitudinal redundancy check' LRC) character.Geometric codes are similar to the XMODEM error-detection technique in thefact that they are also far from foolproof. As an example of this,suppose a 2-bit