Error Detection and Correction Single-bit error Multiple-bit error

Error Detection and CorrectionErrorsดร. อนันต ผลเพิ่มAnan Phonphoem, Ph.D.anan@cpe.ku.ac.thhttp://www.cpe.ku.ac.th/~ananComputer Engineering DepartmentKasetsart University, Bangkok, ThailandSingle-Bit Multiple-Bit Burst1Single-bit errorMultiple-bit error34

Vertical Redundancy Check(VRC) - parityLongitudinal RedundancyCheck (LRC)n bits•Can detect n bits burst error•>n bits can be detected high prob.910VRC and LRCCyclic Redundancy Check(CRC)1112

Binary Division in a CRC gen.Polynomial1314Polynomial and DivisorStandard Polynomials2 properties• Should not divisible by x• Should be divisible by (x+1)1516

CRC• Very effective detection method• Can detect all burst of length < degreeof polynomial• Detect other errors high prob.ChecksumNotes:•Segment•Add using one’s complement•Sum is complemented1718Data Unit and ChecksumWhen the error is detected:• How can we correct them?• Discarded and resent• Automatically correct without resent• In theory, any error binary code can becorrected• But adding complexity• Redundancy• Limited up to 3 errors because of overhead1920

Error CorrectionNumber of redundancy bit• Total bit = m+r• r must be able to indicate all positionsincluding no error m+r+1• r bit can indicate 2 r states• So 2 r >= m+r+1• For ASCII (7bits) m=7• 2 4 >= 7+4+12122Hamming CodeHamming Code• Example: 7-bit ASCII needed r = 42324

Hamming CodeExample of Hamming CodeEach bit iscoveredby at least2checkers2526Single-bit errorError Detection2728