Noise and bandwidth limitations of communication channels cause errors in transmission ofdigital signals. The errors in binary digital transmission are usually measured in Bit Error Rate(BER) which is an average of error bits measured over some statistically significant period ofdata transmission.
Relatively high BER and burst errors are quite common in radio channels where Signal-to-noiseratio (S/N) is a major factor and is closely linked to the fade margin of the radio channel.
The most common way of dealing with noisy communication channels is to divide the data intoframes and send a few extra bytes of check-sum information with each transmitted frame. Thecheck-sum is a numeric value computed from the data being transmitted. The check-sum is thenused by a receiver to verify the correctness of the received data. This method of data verificationis called error detection.
There are several methods to perform error detection. The most common are: Byte Parity entails addition of a bit to each byte. This bit is one (“1”) if the byte contains an even(odd) number of “1” bits. The method is therefore called Even (Odd) Parity. This methodprovides some verification, but many of the errors remain undetected.
In a variation of the byte parity method, several bytes of data are grouped into a block. Anadditional parity byte is appended to each block of data (block parity). This method suffers fromlimitations similar to Byte Parity.
The most powerful error detection method is the CRC. This method is based on results from thecyclic group theory and is the most reliable means for error detection. The MOSCAD RTUsupports the CRC error detection as described below.
The MOSCAD RTU transmits its information and acknowledgments in frames. The length of theframe is variable. This length varies from 7 bytes (excluding CRC) for a short acknowledgmentto a maximum of 200 bytes for a full data frame.
The MOSCAD RTU offers an extraordinary level of error detection and it supports two types ofcommonly known and internationally acknowledged error detection mechanisms: CRC-16 for line communication and RS-232 asynchronous interface CRC-32 for radio communication and RS-232 synchronous interface The MOSCAD RTU has also a built-in efficient Automatic Repeat Request (ARQ) mechanismwhich causes selective retransmission of a corrupted frame.
CRC-16 is a remainder of a polynomial division, modulo two. This is a 16-bit number definedby the CCITT V.41 standard. The polynom is: The minimum Hamming distance of this error detection code is 4. It means that any two validframes of equal length will differ in at least four bits.
100% of all burst errors (several adjacent bits are garbled) of length 16 or less 99.9969% of all burst errors 17 bits long 99.9985% of all burst errors longer than 17 bits So, in fact, the undetected BER is virtually 0 for most types of errors.
On top of that MOSCAD has a selective re-transmission mechanism (retransmission of errorframes only) which improves the throughput immensely.
The CRC-32 bit polynom is (as defined by the IEEE 802.3 standard): X32+X26+ X23+ X22+ X16+ X12+ X11+ X10+ X8+ X7+ X5+X4+ X2+ X+1 This polynom is used for protection of frames, where the total number of bits is less than 12,144(including CRC) as specified by the IEEE 802.3 standard. Under this constraint, the minimumHamming distance of the code is 4.
In MOSCAD RTUs the maximum length of a frame is 1,632 bits (200 bytes/frame * 8bits/byte +32 CRC bits). Under this condition, the minimum Hamming distance is 5. The Hammingdistance increases with decreasing frame lengths.
100% of all burst errors (several adjacent bits are garbled) of length 32 or less 99.999999953% of all burst errors 33 bits long 99.999999976% of all burst errors longer than 33 bits Therefore Virtually no errors will remain undetected with the use of CRC-32.
Peterson, W. " Cyclic Codes for Error Detection.", Proc. IRE, Jan 1961, pp. 228-235.
Cambell, Joe. C Programmers Guide to Serial Communications. Indianapolis, Ind.:Howard W. Sams, 1988 CCITT V.41: Code Independent Error Control, Blue Book, Volume VIII, Facsile VIII-1,1988 ANSI/IEEE Standard for Local Area Networks, “Carrier Sense Multiple Access withCollision Detection (CSMA/CD) Access Method and Physical Layer Specification”, 1984 T. Fujiwara et al. “Error Detecting Capabilities Of The Shortened Hamming CodesAdopted For Error Detection In IEEE Standard 802.3”, IEEE Transactions onCommunications, Vol. 37, No. 9, September 1989, pp 986-989.

Source: http://www.adut.hr/scadadocs/Literature/TechnicalNotes/MOSCAD%20Cyclic%20Redundancy%20Check%20(CRC)%20Mechanism.pdf

Edward m. barnett

Curriculum Vitae—Andrew J.W. Huang, M.D., M.P.H. Address: Department of Ophthalmology and Visual Sciences Washington University School of Medicine 660 South Euclid Avenue, Campus Box 8096 St. Louis, MO 63110 USA Telephone 314-362-3937 Fax 314-362-0627 E-mail huanga@vision.wustl.edu Present Position: Professor of Ophthalmology and Visual Sciences Washington University School of Me

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