Methods to Gain Reliability in Software

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Methods to Gain Reliability
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detection of the existence of a character, especially on tapes Figure 11-1a shows odd-parity encoding for some 8-bit characters on a 9-track tape Odd parity produces a code with a minimum Hamming weight of 1 The counting of bits is done easily by computer hardware, and some machines have speci c instructions for bit counting Most machines perform the encoding and checking processes, until an error occurs, without user intervention The addition of the one parity bit doubles the number of possible symbols that a code can transmit Half of these codes are not valid characters and should not occur in the received input Their appearance hence signals an error condition The number of bits which are di erent between the intended and actual code received is termed the Hamming distance of the two codes The Hamming distance is, of course, equal to the di erence in the Hamming weights of the two codes Simple parity coding is well suited to the communication-oriented processes in computing Parity coding is independent of the content of the data This is both an advantage, in that it can be universally applied, and a disadvantage, since it cannot detect errors related to the content of the data Techniques similar to parity encoding are also used for numbers which are transmitted outside of computer systems Decimal identi cation numbers may have check digits appended which are veri able Since accidental transposition of digits is a frequent error, the check digit is best computed not as a simple sum but as a sum of products as shown in Fig 11-1b Only a one-digit remainder of the sum is retained for checking An interchange of 3 and 4 in the sample will generate a check digit p = 0 instead of p = 1 Many systems invert the check digit to simplify checking, so that p = 1 becomes 9 Modulo 10, as used in Fig 11-1b, will not detect certain transposition errors between alternate columns; in the sample a transposition of 5 and 0 will not be detected Because of the high frequency of transposition errors, use of modulo 9 or 11 (p = 10 0) is preferred even though it reduces the power of the check
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Sec 11-2
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Redundancy
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digit Digits in the position equal to the modulus are not checked at all using the simple successive arithmetic weights scheme Alternate weight assignments which have been used are also shown in Fig 11-1b; the series (1, 10, 1, ) is obtained in e ect by division of the number by 11 Only detection is provided by parity encoding, and even the detection capability is limited Whereas with simple parity all one-bit errors will be detected, reversals of an even number of bits within a single character will not be noted In situations where errors are apt to occur in batches or bursts, the detection probability remains high since a number of sequential characters will be a ected, many of which will have a detectable parity error
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11-2-2 Duplication Duplication of data is another simple form of achieving redundancy It is used during input, in some tape systems, and in the storage of critical data If the data are processed through di erent channels and then matched, the error-detection probability will be quite high To decide which copy to use for correction requires another indicator, for instance, a parity error This approach is hence mainly e ective for hardware faults, program faults will create the same error in both paths The cost of duplicate entry and maintenance of data is, of course, quite high Keypunching with subsequent veri cation of the punched cards by retyping and matching is an example of duplication of data during one small interval of the informationprocessing cycle The original document must remain available to arbitrate when an error is found When information is copied or transmitted, a duplicate will exist for some length of time It can be useful to design the system so that this duplicate remains available until correctness of the copy has been veri ed The detection of an error can be used to initiate recopying of the data This technique is prevalent in the transmission of data over transmission lines Not only is the vulnerability of data during transmission high, but the size of the damaged areas is frequently large A reason for errors to occur in bursts is that the data are transmitted serially, using separate clocks, one on each end, which are used to de ne the individual bit positions A relatively long time will be required to resynchronize these clocks after a timing error Burst errors are also caused by transients induced when lines are being switched in the dial-telephone network Maintenance of completely duplicate les on disks is rarely feasible on generalpurpose computers The cost of completely duplicated storage and of extra channel capacity may also be excessive if one considers the current high reliability of computer storage devices Complete data redundancy also increases the time required for le update The computer systems designed for non-stop operation have fully duplicated channels and controllers to avoid delays in writing to duplicated or mirrored disk units To achieve much of the reliability that a duplicated system can provide, a small amount of selected critical information may be replicated In a le system, this may be the index information or the linkage between records The damage due to loss of a data element can be expected to be minor compared with the e ect of the loss
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